We consider newly derived proper motions of the HH 34 jet to reconstruct the evolution of this outflow. We first extrapolate ballistic trajectories for the knots (starting from their present-day positions and velocities) and find that at similar to 1000 yr in the future most of them will merge to form a larger-mass structure. This mass structure will be formed close to the present-day position of the HH 34S bow shock. We then carry out a fit to the ejection velocity versus time reconstructed from the observed proper motions (assuming that the past motion of the knots was ballistic) and use this fit to compute axisymmetric jet simulations. We find that the intensity maps predicted from these simulations do indeed match reasonably well the [S II] structure of HH 34 observed in Hubble Space Telescope images.