Abstract The dependence of wall mass and energy on wall velocity in thin Permalloy films is calculated by generalizing the Ritz model of Jakubovics (1978) for two-dimensional Bloch walls. In films 1000 A thick, at low velocities, the wall mass is found to be about 52 times the value expected in bulk Permalloy. The mass increases with increasing velocity, v. Up to v≃3 × 104cm s−1 the increase is similar to that of a relativistic mass, namely proportional to (1−v 2/v ∞ 2)−½, with a critical velocity v ∞ ≈ 14.6 × 104 cm s −1 . For v 3 × 104 cm s−1 the increase of mass with velocity becomes more rapid. The model breaks down for velocities above ≃ 6 × lO4cm s−1.