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The paper considers a mathematical model for pulsation process of spherical underwater gas explosion products in a hole during gas-impulse regeneration of filters. A second-order differential equation with constant coefficients has been derived in the paper. A special calculation program has been developed to solve the equation. Expressions have been obtained to calculate a maximum radius of a spherical explosion chamber at the end of expansion process and pressure impulse during the first half-cycle of the pulsation.