© 2014 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society. We present dynamical modelling of the broad-line region (BLR) for a sample of five Seyfert 1 galaxies using reverberation mapping data taken by the Lick AGN Monitoring Project in 2008. By modelling the AGN continuum light curve and Hβ line profiles directly, we are able to constrain the geometry and kinematics of the BLR and make a measurement of the black hole mass that does not depend upon the virial factor, f, needed in traditional reverberation mapping analysis. We find that the geometry of the BLR is generally a thick disc viewed close to face-on. While the Hβ emission is found to come preferentially from the far side of the BLR, the mean size of the BLR is consistent with the lags measured with crosscorrelation analysis. The BLR kinematics are found to be consistent with either inflowing motions or elliptical orbits, often with some combination of the two. We measure black hole masses of log10(MBH/M⊙) = 6.62-0.13+0.10 for Arp 151, 7.42-0.27+0.26 for Mrk 1310, 7.59-0.21+0.24 for NGC 5548, 6.37-0.16+0.21 for NGC 6814, and 6.99-0.25+0.32 for SBS 1116+583A. The f factors measured individually for each AGN are found to correlate with inclination angle, although not with MBH, L5100, or FWHM/s of the emission line profile.