In many respects, accelerometers are convenient for measuring the lateral vibrations of a gun tube under impulse loads. Reliable measurements by accelerometers must overcome two issues: exceedingly large acceleration at high frequencies due to stress waves, and the elimination of drifts accumulating through the integration of acceleration signals. In this paper, we use a mechanical filter that reduces the effect of stress waves. Also, we propose a new double integration algorithm based on multi-resolution wavelet decomposition. Using a test-rig, we measure the vibration characteristics of commercially-available damping materials. Based on the test results, we design a mechanical filter and experimentally verify the performance of the filter. The proposed double integration algorithm is shown to be as effective as other existing algorithms without arbitrary selection of parameters.