The concept for a novel new antenna design is presented and investigated for application to ground penetrating radar (GPR). The proposed new antenna design is called the shielded magnetic bowtie antenna (MBA). As the name suggests, it is predominately constructed from a bowtie-shaped volume of magnetic material that is fed from the centre of the structure by a small magnetic loop antenna. This thesis develops the magnetic antenna concept and investigates its potential for GPR predominately through numerical modelling. However, a significant part of the investigation concentrates on validating the numerical modelling technique developed to study the shielded MBA by comparing the results with measurements obtained from a scale model constructed to operate in the watertank antenna test facility, a controlled environment for GPR antenna research. The broadband properties required for GPR antennas are achieved uniquely with the shielded MBA design by a combination of the antenna shape being defined in terms of angles and an inherent magnetic loss mechanism within the antenna material structure. The design also affords an intrinsically placed antenna shield that has the potential for mitigating problems typically experienced with shielding electric dipole antennas. Antenna shielding is an important consideration for GPR antenna designers, especially given the recent US government (FCC) changes that restrict radiated energy emissions within the regulated spectrum used by GPR systems. In addition to providing the intended directional radiation properties, the magnetic antenna shield also provides an elegant solution for a low-loss wideband balun, allowing the antenna to be effectively fed from an unbalanced coaxial transmission line. Other important aspects of the proposed design are discussed in relation to the requirements for GPR antennas. Numerical models of the magnetic antenna concept show encouraging bandwidth results. For example, from a simple comparison with an equivalent sized electric bowtie antenna model, the effective gain bandwidth of the magnetic antenna is found to be at least 3-octaves compared to approximately 2-octaves for the electric bowtie. The shielded magnetic antenna achieves a gain of approximately 2 dB, compared to 5 dB for the unshielded electric bowtie antenna. However, it is noted that the magnetic antenna models contain significantly more loss compared to the electric bowtie model. The shielded MBA design emerged from a theoretical investigation of electrically small GPR antennas, given that the initial thesis objective was to investigate ways of improving low frequency GPR antennas. In general, GPR systems are operated with electric dipole antennas, such as the electric bowtie. Interestingly, the electrically small antenna investigation revealed that only the small magnetic loop (i.e., magnetic dipole) antenna can be constructed to approach, arbitrarily closely, the fundamental bandwidth limit for small antennas. This surprising and counter intuitive result is shown to be theoretically achievable with the use of magnetic materials. For the small loop antenna, energy stored within the antenna structure can be avoided by filling the antenna sphere with a perfect magnetic material. This theoretical argument is discussed and supported by numerically modelled results. The electrically small antenna investigation presented in this thesis extends to include the influence that proximity to a lossy dielectric half-space has, on improving the antenna impedance bandwidth. This investigation is of general interest for GPR; it is performed numerically and supported by measurements conducted on an experimental loop antenna situated at various heights above the ground. These results provide support for the hypothesis that a magnetic antenna may experience less influence from near-field changes in the dielectric properties of the ground compared to the equivalent sized electric field antenna.