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For the 2D continuous space-time (CST) systems are described by linear 2-D partial equations, generally, it is impossible to get the closed solutions of the CST systems. To get the space-time response of CST systems needs the inverse 2-D Laplace transform. However, the 2-D inverse Laplace transform (ILT) does not exist for unstable CST, a theorem is proposed to ensure the 2-D ILT to be obtained for stable CST systems. In this paper, we present the approach to get the solutions of CST systems, we also derive an algorithm of numerical 2-D ILT for the vector spatial-time response analysis of CST systems.