Browse 20 apartments for rent with an elevator in Converse, TX. Apartment buildings with elevators provide convenience during move-in, move-out, and during your stay. When you rent an apartment with an elevator, you won't have to worry about hauling furniture or suitcases up the stairs, lugging groceries up multiple stories, or preparing to climb several flights after a long day at work. Not to mention, buildings with elevators tend to be newer or recently updated, meaning you could enjoy more contemporary finishes and efficient layouts.