The results of Monte Carlo radiation shielding study performed with the MARS15 code for the vertical test facility at the A0 north cave enclosure at Fermilab are presented and discussed. The vertical test facility at the A0 north cave is planned to be used for testing 1.3 GHz single-cell superconducting RF cavities with accelerating length of 0.115 m. The operations will be focused on high accelerating gradients--up to 50 MV/m. In such a case the facility can be a strong radiation source. When performing a radiation shielding design for the facility one has to take into account gammas generated due to interactions of accelerated electrons with cavity walls and surroundings (for example, range of 3.7-MeV electrons in niobium is approximately 3.1 mm while the thickness of the niobium walls of such RF cavities is about 2.8 mm). The electrons are usually the result of contamination in the cavity. The radiation shielding study was performed with the MARS15 Monte Carlo code. A realistic model of the source term has been used that describes spatial, energy and angular distributions of the field-emitted electrons inside the RF cavities. The results of the calculations are normalized using the existing experimental data on measured dose rate in the vicinity of such RF cavities.