UV radiation exerts several effects concerning life on Earth, and spectral information on the prevailing UV radiation conditions is needed in order to study each of these effects. In this paper, we present a method for reconstruction of solar spectral UV irradiances at the Earth's surface. The method, which is a further development of an earlier published method for reconstruction of erythemally weighted UV, relies on radiative transfer simulations, and takes as input (1) the effective cloud optical depth as inferred from pyranometer measurements of global radiation (300-3000 nm); (2) the total ozone column; (3) the surface albedo as estimated from measurements of snow depth; (4) the total water vapor column; and (5) the altitude of the location. Reconstructed daily cumulative spectral irradiances at Jokioinen and Sodankylä in Finland are, in general, in good agreement with measurements. The mean percentage difference, for instance, is mostly within +/-8%, and the root mean square of the percentage difference is around 10% or below for wavelengths over 310 nm and daily minimum solar zenith angles (SZA) less than 70 degrees . In this study, we used pseudospherical radiative transfer simulations, which were shown to improve the performance of our method under large SZA (low Sun).