Finite thin disc models of four galaxies in the Ursa Major cluster are presented. The models are obtained by means of the Hunter method and the particular solutions are chosen in such a way that the circular velocities are adjusted very accurately to the observed rotation curves of some specific spiral galaxies. We present particular models for the four galaxies NGC 3877, NGC 3917, NGC 3949 and NGC 4010 with data taken from the recent paper by Verheijen & Sancici. By integrating the corresponding surface mass densities, and considering all the mass as concentrated at the galactic disc, we obtain the total mass of these galaxies and for all of them we obtain values of the order of 1010 M⊙. Accordingly, these values for may be taken as a quite accurate estimate of an upper bound to the disc mass of these galaxies and a lower bound to their total mass. These models can be considered as a first approximation to obtaining quite realistic models of spiral galaxies.