We present a self consistent nonparametric model of the local cosmic velocity field based on the density distribution in the PSCz redshift survey of IRAS galaxies. The error analyisis, carried out on mock PSCz catalogues constructed from N-body simulations, reveals uncertainties of ~70 km/sec. The denser sampling provided by the PSCz survey compared to previous IRAS galaxy surveys allows us to reconstruct the velocity field out to larger distances. The most striking feature of the model velocity field is a coherent large-scale streaming motion along a baseline connecting Perseus-Pisces, the Local Supercluster, the Great Attractor, and the Shapley Concentration. We find no evidence for back-infall onto the Great Attractor. Instead, material behind and around the Great Attractor in inferred to be streaming towards the Shapley Concentration The PSCz model velocities compare well with those predicted from the 1.2Jy redshift survey of IRAS galaxies and with those predicted from the distribution of Abell/ACO clusters, out to 140 Mpc/h. Comparison of the real-space density fields (or, alternatively, the peculiar velocity fields) inferred from the PSC$z$ and cluster catalogues gives a relative (linear) bias parameter between clusters and IRAS galaxies of 4.4 +/- 0.6. Finally, we compare the cumulative bulk flows predicted from the PSCz gravity field with those measured from the Mark III and SFI catalogues of peculiar velocities. A conservative estimate of beta=Omega**0.6/b, where b is the bias parameter for IRAS galaxies, gives beta =0.76 +/- 0.13, in agreement with other recent determinations.