The Martian surface is constantly exposed to a high dose of cosmic radiation consisting of highly energetic particles and multiple types of ionizing radiation. The dose can increase temporarily by a factor of 50 through the occurrence of highly energetic solar flares. This may affect crop growth in greenhouses on the Martian surface possibly making settlement of humans more complicated. Shielding crops from radiation might be done at the expense of lighting efficiency. However, the most energy-efficient cultivation may be achieved through the use of natural daylight with the addition of LED lights. The goal of our research was to investigate whether Martian radiation, both the constant and the solar flares events, affects plant growth of two crop species, rye and garden cress. The levels of radiation received on the surface of Mars, simulated with an equivalent dose of ⁶⁰Co γ-photons, had a significant negative effect on the growth of the two crop species. Although germination percentages were not affected by radiation, biomass growth was significantly decreased by 32% for cress and 48% for rye during the first 4 weeks after germination. Part of the biomass differences may be due to differences in temperature between radiation and control treatment, however it cannot explain the whole difference between the treatment and control. Coloring of leaves, necrosis and brown parts, was observed as well. Temporary increases in ionizing radiation dose at different development stages of the plants did not significantly influence the final dry weight of the crops.