The stellar disc kinematics in a sample of 15 intermediate- to late-type edge-on spiral galaxies are studied using a dynamical modelling technique. The sample covers a substantial range in maximum rotation velocity and deprojected face-on surface brightness and contains seven spirals with either a boxy- or peanut-shaped bulge. Dynamical models of the stellar discs are constructed using the disc structure from I-band surface photometry and rotation curves observed in the gas. The differences in the line-of-sight stellar kinematics between the models and absorption-line spectroscopy are minimized using a least-squares approach. The modelling constrains the disc surface density and stellar radial velocity dispersion at a fiducial radius through the free parameter root M/L (sigma(z)/sigma(R))(-1), where sigma(z)/sigma(R) is the ratio of vertical and radial velocity dispersion and M/L is the disc mass-to-light ratio. For 13 spirals a transparent model provides a good match to the mean line-of-sight stellar velocity dispersion. Models that include a realistic radiative transfer prescription confirm that the effect of dust on the observable stellar kinematics is small at the observed slit positions. We discuss possible sources of systematic error and conclude that most of these are likely to be small. The exception is the neglect of the dark halo gravity, which has probably caused an overestimate of the surface density in the case of low surface brightness discs.