This paper is concentrated to form the exact element matrices for four sided finite elements. The construction of
higher order hybrid type four sided elements with their exact matrices in terms of algebraic expressions is also
focused. The matrices are formed in such a way that no integration is required. The numerical integration scheme,
such as Gaussian quadrature takes large number of Gaussian points for higher accuracy. But more number of
Gaussian points makes the scheme inefficient. Hence to make a proper balance between accuracy and efficiency, the
elements of simple shapes for which the components of matrices are exactly known, are used by well known
assembly process to form the desired matrices for four sided elements. Hence, algebraic expressions in terms of
nodal coordinates are presented and for their computation, a code is developed. Several examples available in the
literatures are considered to test the exactness and efficiency of the calculation of element matrices with these
developed expressions. In all cases, it is observed that the present technique is faster and exact. Thus, we believe that
this study will contribute directly to the finite element method solution procedure for continuum mechanics
problems to obtain desired accuracy in the solutions.