The problems of the elastic theory need a series of partial differential equations. It always meet with difficulties in math. So we have to seek for approximate solution. The approximate solution of variational calculus is a method in common use. In math, variational problems are the problems to solve the limit of the functional. In elastic mechanics. the functional is the energy( work) of elasticity problems. And the variational calculus is to s calculate the extremum of the energy ( work). We can yield the solution of the elastic problems when calculating the extremum. The direct method of variation problems facilitate us to obtain the approximate solution We will give the expressions which calculate the potential energy of strain at first in this chapter. We will mainly introduce the variational method of displacement and that of stress through the relation of work and energy5 The problems of the elastic theory need a series of partial differential equations. It always meet with difficulties in math. So we have to seek for approximate solution. The approximate solution of variational calculus is a method in common use. In math, variational problems are the problems to solve the limit of the functional. In elastic mechanics, the functional is the energy(work) of elasticity problems. And the variational calculus is to calculate the extremum of the energy(work). We can yield the solution of the elastic problems when calculating the extremum. The direct method of variation problemsfacilitate us to obtain the approximate solution. We will give the expressions which calculate the potential energy of strain at first in this chapter. We will mainly introduce the variational method of displacement and that of stress through the relation of work and energy