Micro-plates exhibit extraordinarily low losses in viscous fluids when vibrating in the non-conventional roof tile-shaped modes. However roof tile-shaped modes are commonly not considered for micro-sensors due to the lack of methods to predict these modes’ dynamic response in viscous fluids. We developed a numerical method to calculate the spectral displacement of micro-plates oscillating in viscous fluids with which we can predict both conventional and non-conventional vibrational modes. The method is based on the Kirchhoff-Love plate equation, which we solve with a continuous-discontinuous approach to the Galerkin Method, with the method of fundamental solutions for the linearized Navier-Stokes equations. We show-case our method with the analysis of a silicon micro-plate immersed in water. With the spectral displacement curve it is straight forward to categorize peaks correspondent to beam bending modes, torsional modes and roof tile-shaped modes. Furthermore, we calculate the fluid flow field associated to each vibrating mode of the micro-plate. Our method thus provides a crucial understanding of the flow field around an oscillating micro-plate, which may enable novel device architectures for resonantly operated micro-sensors in viscous fluids.