Gilbert Square Apartments for rent in Mesa, AZ on ForRent.com: (866) 279-9624 - Availability, pricing and special promotions subject to change daily. Welcome to Gilbert Square Apartments. Discover the perfect choice for your new home. The prime location to enjoy a wide range of community conveniences-- shopping, banks, post office, restaurants and entertainment. If you have been searching for a community offering comfortable living at affordable prices, then look no further than Gilbert Square.