The thesis discusses the possibility of using ultrawideband (UWB) radar to detect breast cancer. At the present time, X-ray mammography and ultrasound are the golden standard imaging techniques for detection and evaluation of breast cancer, but they both have their limitations. The primary aim of this thesis is to use ultrawideband planar elliptical antennas in the detection of breast cancer, and investigate the use of the delay-and-sum beamforming technique applied on both the receiver (Rx) and transmitter (Tx). At first, a description of the antenna and its basic characteristics are given. Then, models consisting of four identical antennas with a layer of fat between them and a tumor inside were constructed. Simulations were performed with the tumor placed on three different locations. In many of the models and parameters used and tested here, the Tx-Rx method is equal to or better than the Rx method to detect breast cancer. This work should be of interest to people working with UWB technology and similar research areas.