Delivery of subnanosecond pulses into biological tissue can be undertaken by an impulse radiating antenna (IRA). Previous analysis shows that it is important to add a dielectric lens, which reduces the abrupt change of dielectric constant from air to tissue and therefore increases the transmission of the pulses. As a proof of concept, we have simulated subnanosecond pulsed radiation focused into a tissue simulant which consists of homogeneous, hemisphere tissues using 3-D electromagnetic solver, CST Microwave Studio. The simulation of an IRA in conjunction of a lens indicates subnanosecond pulses can be focused 6 cm below tissue surface with a spot diameter approximately 1 cm. The focal point coincides with the geometric focus of the IRA. However, this result is only valid for a tissue with a low conductivity (V< 0.3 S/m). For lossier tissues, the electric field decreases from the surface monotonically as the subnanosecond pulses penetrate in depth. Two approaches were proposed to solve this problem. One was to use an inhomogeneous dielectric lens, with lossy material partially filled, to attenuate the incident field in the small azimuthal angles but to spare the field in the larger azimuthal angels. A desirable focusing was observed. The second approach was to use a dipole antenna in conjunction with the impulse radiating antenna. The dipole antenna decreases the surface field intensity generated by the aperture antenna, but at the destination, the field will be mostly given by the aperture antenna, resulting in a focusing.