Fifth generation (5G) wireless networks are expected to utilize wide bandwidths available at millimeter wave (mmWave) frequencies for enhancing system throughput. However, the unfavorable channel conditions of mmWave links, e.g., higher path loss and attenuation due to atmospheric gases or water vapor, hinder reliable communications. To compensate for these severe losses, it is essential to have a multitude of antennas to generate sharp and strong beams for directional transmission. In this paper, we consider mmWave systems using uniform planar array (UPA) antennas, which effectively place more antennas on a two-dimensional grid. A hybrid beamforming setup is also considered to generate beams by combining a multitude of antennas using only a few radio frequency chains. We focus on designing a set of transmit beamformers generating beams adapted to the directional characteristics of mmWave links assuming a UPA and hybrid beamforming. We first define ideal beam patterns for UPA structures. Each beamformer is constructed to minimize the mean squared error from the corresponding ideal beam pattern. Simulation results verify that the proposed codebooks enhance beamforming reliability and data rate in mmWave systems.