Recently, as high-rise buildings increase steeply, sub-structures of them are often supported on in-homogeneous foundation. And there are many machines in sub-structures of buildings, and slabs of sub-structures are affected by vibration which they make. This paper deals with vibration of plates with concentrated masses on in-homogeneous foundation. Machines on plates are considered as concentrated masses. In-homogeneous foundation is considered as assigning $k_{w1}$ and $k_{w2}$ to Winkler foundation parameters of central region and side region of plate respectively, and foundation is idealized to use Pasternak foundation model which considered both of Winkler foundation parameter and shear foundation parameter. In this paper, applying Winkler foundation parameters which $k_{w1}$and $k_{w2}$ are 10, $10^2$, $10^3$ and shear foundation parameter which are 10, 20 respectively, first natural frequencies of thick plates with concentrated masses on in-homogeneous foundations are calculated.