For a magnetic-fluid membrane, the critical pressure drop is determined experimentally using thermodynamic and hydrostatic methods. It is found that the value of the critical pressure drop calculated from the data of the thermodynamic method exceeds by similar to 30% the value of this parameter measured by the hydrostatic method. The overstated value of the critical pressure drop obtained using the indirect thermodynamic method is explained by the approximate nature of the analytical model lying at its basis, which does not take into account the relaxation character of pondermotive elasticity. The static and thermodynamic coefficients of pondermotive elasticity of a magnetic-fluid membrane sample are calculated, and the results are used to estimate the membrane displacement by the moment of its breakage.