We report new radial velocity observations of GP Vel/HD77581, the optical companion to the eclipsing X-ray pulsar Vela X-1. Using data spanning more than two complete orbits of the system, we detect evidence for tidally induced non-radial oscillations on the surface of GP Vel, apparent as peaks in the power spectrum of the residuals to the radial velocity curve fit. By removing the effect of these oscillations (to first order) and binning the radial velocities, we have determined the semi-amplitude of the radial velocity curve of GP Vel to be K_o=22.6+/-1.5 km/s. Given the accurately measured semi-amplitude of the pulsar's orbit, the mass ratio of the system is 0.081+/-0.005. We are able to set upper and lower limits on the masses of the component stars as follows. Assuming GP Vel fills its Roche lobe then the inclination angle of the system, i=70.1+/-2.6 deg. In this case we obtain the masses of the two stars as M_x=2.27 +/-0.17 M_sun for the neutron star and M_o=27.9+/-1.3 M_sun for GP Vel. Conversely, assuming the inclination angle is i=90 deg, the ratio of the radius of GP Vel to the radius of its Roche lobe is beta=0.89+/-0.03 and the masses of the two stars are M_x=1.88+/-0.13 M_sun and M_o=23.1+/-0.2 M_sun. A range of solutions between these two sets of limits is also possible, corresponding to other combinations of i and beta. In addition, we note that if the zero phase of the radial velocity curve is allowed as a free parameter, rather than constrained by the X-ray ephemeris, a significantly improved fit is obtained with an amplitude of 21.2+/-0.7 km/s and a phase shift of 0.033+/-0.007 in true anomaly. The apparent shift in the zero phase of the radial velocity curve may indicate the presence of an additional radial velocity component at the orbital period. Comment: Accepted for publication in Astronomy & Astrophysics