This thesis focuses on mobile phones antenna design with brief description about the historical development, basic parameters and the types of antennas which are used in mobile phones. Mobile phones antenna design section consists of two proposed PIFA antennas. The first design concerns a single band antenna with resonant frequency at GPS frequency (1.575GHz). The first model is designed with main consideration that is to have the lower possible PIFA single band dimensions with reasonable return loss (S11) and the efficiencies. Second design concerns in a wideband PIFA antenna which cover the range from 1800MHz to 2600MHz. This range covers certain important bands: GSM (1800MHz & 1900MHz), UMTS (2100MHz), Bluetooth & Wi-Fi (2.4GHz) and LTE system (2.3GHz, 2.5GHz, and 2.6GHz). The wideband PIFA design is achieved by using slotted ground plane technique. The simulations for both models are performed in COMSOL Multiphysics.  The last two parts of the thesis present the problems of mobile phones antenna. Starting with Specific absorption rate (SAR) problem, efficiency of Mobile phones antenna, and hand-held environment.