While it may not be possible to completely seal up your home to keep out cockroaches, there are some small focused areas where you can block access. These are a few ways you can create important 'no cockroach zones' in your home.
The food stored in your refrigerator and freezer are probable safe. Cockroaches will avoid the cold and, if the seals on your refrigerator are in good shape, they will not have an easy time getting in (it's not a bad idea to spend some time cleaning the door seals really well - a lot of food ends up spilling in there.) Store what you can in there (my wife and I still keep our coffee in the freezer.)
Canned goods and vacuum sealed items from the grocery store are also safe from infestation - at least until you open them.
For maximum effectiveness, I recommend focusing on the dry-goods storage in your kitchen that you usually open and use a small amount at a time. Cereal, pasta, beans, rice, sugar, flour, and dozens of other similar foods need some extra protection.
Use zipper locking freezer bags (quart and gallon sized), seal-able plastic bins (they make flip-top versions specially for holding cereal), and ceramic crocks and glass storage jars with lids that seal.
The goal is to make sure that all food is stored in an air-tight container. Rolling-up the liner inside a box of cereal leaves plenty of room for a cockroach to get in. Don't give them the option.
Taking steps to protect your food provides additional benefits. Sealing food in airtight packages will preserve freshness and keep out other pantry pests as well.
Teflon tape (also known as thread tape) is used by plumbers to seal the threads of pipes. It looks like white tape, but the Teflon coating is actually very slippery. If you cover 2-3 inches of a table or chair leg with this tape, cockroaches can't get enough grip to walk across it. Since they can't cross the tape line border, they can't get from the floor to the tabletop or chair seat.
During my infestation problem, we wrapped the legs of the baby's high-chair, our dinner table legs, and the legs of our chairs with 3 inches of Teflon tape.
Teflon tape is not sticky to the touch, but it will adhere to itself. It is also very stretchy. To apply it, wrap it once around the leg and pull it taut before overlapping the first layer. Then, wind it around the leg overlapping the previous layer slightly) until you have covered 2-3 inches of the leg. Snap the tape with your fingers and smooth the loose end into the previous layer.
The tape can be removed later by unwinding from the top. It will not leave any residue behind since there is no adhesive.
This simple trick brought huge mental relief to me and my wife during our cockroach infestation.
Cockroaches can move through the drainpipes in your home as well as the walls. If you live in an apartment building where the drains between multiple units are connected, this may be a significant pathway for roaches to move between apartments.
A drain has most of what a cockroach needs - water and food (even bathroom drains will have enough organic material stuck in them to provide a decent meal.) There is a bend in every drain pipe called a p-trap that is designed to hold a small amount of water in it to prevent sewer gases from entering your home through the pipes. Cockroaches are not stopped by the water.
During my infestation problem, I closed my drains every night before going to bed. This kept new cockroaches from entering and any inside the apartment already from getting a drink or meal.
Before bed, I put stoppers in the kitchen sinks and closed the bathroom drain plugs. The tub and bathroom sink drains also have overflow holes that connect to the drain to prevent the sink and tub from overfilling. Cover those with a piece of tape.
I also poured a small amount of bleach into the drains at night. This made the water in the p-traps deadly for the cockroaches to drink or touch. Use caution and follow all manufacturer instructions if you decide to try this. Bleach is a hazardous chemical.
Using bleach is purely optional. Stopping up the drains will prevent the roaches from moving through the pipes.
At the beginning of this report I mentioned that we once found a cockroach crawling on our bed. This is not something you want to see - sleeping soundly becomes a challenge from that point forward. The last thing you need when dealing with a cockroach infestation is to be sleep deprived too.
If you have dust ruffles and long comforters, duvets, or blankets that hang down from your bed to the floor, take them off the bed until you have your infestation under control.
Use bed covers that can be tucked into the mattress to eliminate pathways for the cockroaches to get onto your bed from the floor.
Apply silicon tape to the legs of the bed frame as described earlier, and remove storage items under the bed that might allow roaches to reach the bed frame from the floor.
I went an extra step and placed glue traps under the bed along the walls to catch any cockroaches that might have wandered into the room.