Horizontal Bloch line (HBL) motion in magnetic bubble materials is studied by comparing experimental results with a numerical simulation of domain wall motion. The present theory of HBL motion is reviewed and then extended by allowing both the wall position q and azimuthal angle φ to vary with position through the film thickness z. The resulting equations of motion are solved numerically for q(z, t) and φ(z,t), and the solutions are compared with results from wall oscillation experiments. In these experiments, a bias field pulse is used to produce a step change in the equilibrium position of stripe domain walls in the presence of small in-plane fields parallel to the walls, Hx= 0 Oe, 4 Oe, and 10 Oe. The wall response is then measured by using a sampling photometric technique. Good quantitative agreement is found between numerical and experimental results, so that the internal processes that occur during wall motion can be inferred from the calculation. Changes in q through the film thickness play an important role in HBL motion. During the initial response, the twist structure φ(z) is similar to the initial static structure and the wall surface is relatively flat. A backward bulge soon forms near one of the film surfaces as a result of local dynamic properties. This bulge provides the additional torque necessary to form the HBL. The bulge accompanies the HBL as it moves toward the opposite film surface and provides the torque necessary for HBL propagation. Internal vibrations of the wall surface are excited by the bulge and produce irregular motion of the average wall position. Punch-through occurs when the HBL reaches the opposite surface. During this process, φ at the film surface rotates rapidly from π/2 to 3π/2. At the same time the wall section in this region moves backward. As a result, the average wall position is essentially stationary during punch-through.