  This paper extends the Method of Particular Solutions (MPS) to the
computation of eigenfrequencies and eigenmodes of plates. Specific
approximation schemes are developed, with plane waves (MPS-PW) or
Fourier-Bessel functions (MPS-FB). This framework also requires a suitable
formulation of the boundary conditions. Numerical tests, on two plates with
various boundary conditions, demonstrate that the proposed approach provides
competitive results with standard numerical schemes such as the Finite Element
Method, at reduced complexity, and with large flexibility in the implementation
choices.
