We present dynamical modeling 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 modeling the AGN continuum light curve and H$beta$ 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 disk viewed close to face-on. While the H$beta$ 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 cross-correlation 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 $log_{10}(M_{rm,BH}/M_odot)=6.62^{+0.10}_{-0.13}$ for Arp 151, $7.42^{+0.26}_{-0.27}$ for Mrk 1310, $7.51^{+0.23}_{-0.14}$ for NGC 5548, $6.42^{+0.24}_{-0.18}$ for NGC 6814, and $6.99^{+0.32}_{-0.25}$ for SBS 1116+583A. The $f$ factors measured individually for each AGN are found to correlate with inclination angle, although not with $M_{rm,BH}$, $L_{5100}$, or FWHM/$sigma$ of the emission line profile.
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