The present work deals with optimisation of free vibration of fibre reinforced composite rectangular plates. In this investigation, Eglass/epoxy and Jute/epoxy rectangular plates were fabricated using hand lay-up technique. Experimental mechanical testing was done as per ASTM standard for the plates and elastic properties such as Young's modulus, Poisson's ratio and shear modulus were carefully calculated from the test data. For the same specimens, elastic properties were derived using analytical method by rule of mixture and Chamis model. These data were fed into finite element analysis in ANSYS software to find the natural frequencies and mode shapes. Finite element analysis as the result of experimental mechanical testing and analytical model for both plates were compared and dynamic characteristics were discussed elaborately. The effects on aspect ratio (a/b = 3.75, 7.5) for both plates on natural frequency were studied experimentally using hammer method. Finally the cause for the difference in natural frequency and mode shapes were justified with available data.