A 3D Finite Element Boundary Integral technique (FE-BI) using mixed-order tangential vector finite elements (TVFE?s) is presented. This technique is used to design two wide band antennas and an ultra wideband (UWB) antenna array. Tetrahedral elements are used for domain discretization because they offer higher flexibility when simulating complex structures. A set of hierarchical mixed-order TVFE?s up to and including order 2.5 is implemented. Hierarchical mixed-order TVFE?s accurately simulate regions with high and low field variations. They also guarantee tangential field continuity across element boundaries and suppress spurious modes. The efficacy of the technique has been tested on two different wide band antennas and an UWB array. The first antenna is designed for automotive applications and covers GPS, GSM, XM, and PCS bands (0.8?3.35 GHz). The second antenna is a double sided rounded bowtie antenna (DSRBA) for UWB communication (3.1-10.6 GHz). The third design is a DSRBA array. For validation purposes, the antennas are also simulated using a commercially available high frequency electromagnetic simulation software, HFSS. Results regarding antenna parameters such as return loss, radiation pattern, and gain are also given.