In this paper the fundamental solutions for an infinite poroelastic moderately thick plate and analytical solutions for a circular plate saturated by a incompressible fluid are derived in the Laplace transform domain. In order to obtain the solutions in the time domain, the Durbin’s Laplace transform inverse method has been used with high accuracy. The formulations using the boundary integral equation method can be derived directly with these fundamental solutions. In addition, the analytical solutions for a circular plate can be used to validate the accuracy of numerical algorithms such as the boundary element method and the method of fundamental solution. The deflection, moment, and equivalent moment in the time domain for a circular plate, subjected to uniform load and a concentrated force are presented, respectively. The analytical solutions demonstrate that interaction between the solid and flow is significant.