In this work, we have devised a new approach to measure the critical pressure that a liquid marble can withstand. A liquid marble is gradually squeezed under a mechanical compression applied by two parallel plates. It ruptures at a sufficiently large applied pressure. Combining the force measurement and the high-speed imaging, we can determine the critical pressure that ruptures the liquid marble. This critical pressure, which reflects the mechanical robustness of liquid marbles, depends on the type and size of the stabilizing particles as well as the chemical nature of the liquid droplet. By investigating the surface of the liquid marble, we attribute its rupture under the critical pressure to the low surface coverage of particles when highly stretched. Moreover, the applied pressure can be reflected by the inner Laplace pressure of the liquid marble considering the squeezing test is a quasi-static process. By analyzing the Laplace pressure upon rupture of the liquid marble, we predict the dependence of the critical pressure on the size of the liquid marble, which agrees well with experimental results.