Abstract: An integration depending on a parameter to the compression of a thick workpiece has been obtained. For the conventional prevailing numerical formula a definite functional relationship bet-ween and y is found. Therefore a parametric integration can be used to get an analytical solution. Take the slip line field for l/h= 0.121 as an example, the analytical solution is basically the same as the prevailing numerical one. It is justified theoretically that for the slip line field a parametric integration is perfectly possible for a satisfactory analytical solution.