The UV radiation environment on planetary surfaces and within atmospheres is of importance in a wide range of scientific disciplines. Solar UV radiation is a driving force of chemical and organic evolution and serves also as a constraint in biological evolution. In this work we modeled the transmission of present and early solar UV radiation from 200 to 400 nm through the present-day and early (3.5 Gyr ago) Martian atmosphere for a variety of possible cases, including dust loading, observed and modeled O3 concentrations. The UV stress on microorganisms and/or molecules essential for life was estimated by using DNA damaging effects (specifically bacteriophage T7 killing and uracil dimerization) for various irradiation conditions on the present and ancient Martian surface. Our study suggests that the UV irradiance on the early Martian surface 3.5 Gyr ago may have been comparable with that of present-day Earth, and though the current Martian UV environment is still quite severe from a biological viewpoint, we show that substantial protection can still be afforded under dust and ice.