In elastic mechanics, it is common practice to calculate critical loads in buckle of thin plates by means of double triangle series. The calculation process is more complex, this method has not facility in engineering application. In many cases critical loads of thin plates can not obtain precise analytic solutions. It is very important to solve approximate resolutions of critical loads of plates in engineering. The method of weighted residuals is an available measure to solve proximal resolutions of differential equations and has extensive application in egineering. In order to simplify calculation process and obtain profitble result, by means of method of weighted residuals and Cantorovich variational principle, taking the second Tchebychev's polynomials as trial functions, it was calculated, critical loads of rectangle thin plates in different supporting conditions. Calculation results indicate that this calculation method is simple and has some precision, it is applied conveniently in engineering.