Numerical solutions for the time history of motion of a shallow viscoelastic spherical shell are presented under large deformations. Axisymmetric motion is considered due to uniform pressure with arbitrary time variation. The dynamic viscoelastic buckling load is established by comparing long-time equilibrium states due to small changes in the applied pressure. The problem is formulated as a coupled pair of nonlinear integro-differential equations which is solved by Newton’s method.

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