When use the allowable stress method to calculate a solid rectangular cross section,which was a compression member with large eccentricity ,need to solve a cubic equation about Y which has no quadratic term ：y3+py+q=0(equation(1)). Previous literature on eccentric compression member introduction, focuses on the components of the stress characteristics, failure pattern and the section size, length, material relations and so on, there is little to solve the equation (1 ) states, in fact the solution of equation (1) directly determines the results of the cross section calculation .This paper using higher mathematics principle detailed analysis the solution of equation(1) from the mathematical point of view. enumerate solutions exist eight cases：1. p>0 q>0,2. p >0 q <0 3．p <0 q >0 fmin<0 ,4. p <0 q >0 fmin>0,5. p <0 q >0 min=0,6. p <0 q <0 fmax<0,7. p <0 q <0 fmax>0,8.p <0 q <0 fmax=0, combined with the engineering application calculation, induction, summary of many large eccentric compression member has been done; put forward opinions of eight cases, especially should pay attention to the solution of the third case , this case has two positive solutions, solving the undeserved may get the wrong result, the designer should pay special attention to it..