In this work, polynomial deflection expression was used in the free-vibration investigation of thick rectangular plates with two different boundary conditions; one with its four edges clamped denoted with the acronym (CCCC) and another with two adjacent edges fixed and having simple supports at the other two adjacent edges denoted with the acronym (CCSS). The edge conditions of the various plates were fulfilled and used in generating the stiffness coefficients which were substituted into the analytical equation to obtain the non-dimensional frequency functions for the plates at different span-depth ratio (a/t) and aspect ratio (b/a). It was observed that at the same value of (b/a), there is an increase in the value of the non-dimensional frequency parameter as (a/t) increases. Also, at the same value of (a/t), there is a decrease in the value of the non-dimensional frequency parameter as (b/a) increases. The results obtained for the all edges clamped plate were compared with similar works by other researchers in the literature and were found to follow similar pattern and trend and were quite close.