The principle underlying expression basically involves the separation of a solid from the liquid in which it is suspended by passing the mixture through a porous medium with pore sizes too small to allow the passage of the solid particles at an applied pressure. The analytical method of the finite element method has been used to determine pressure, displacement and concentration distribution along sludge cake height in a filter press expression process. The ranges of displacement in a sludge cake height with increase time of expression increases with a decrease in sludge depth. The displacement increases continuously with increase time of expression. The finite element formulation basically involves the properties of the sludge in question as distinguished from other solution. The solution domain was idealized as a one-dimensional quadratic shape function for the purpose of this analysis and the displacement function formulation method were employed in solving the pressure distribution. The results of the finite element solution further showed that concentration increases with decreasing height of sludge cake interface during sludge dewatering. There is however an increasing tendency to uniformity of concentration with increment in the time of expression.