In solving displacement of non-uniform beams,all of the textbooks and documents about mechanics of materials expatiate upon uniform beams,whose flexural rigidity EI is constants,while seldom about non-uniform beams.But non-uniform beams whose flexural rigidity EI is variable quantity,are very popular in the practical engineering.When we calculate for rigidity of the non-uniform beams,we achieve firstly equations of deflection curve by making use of various methods.Then obtain the maximum displacement through solving equations.Finally we check the rigidity of non-uniform beams and make it to be safety and reliability.Methods of unit force,integration and the least potential principle is put forward for solving displacement of non-uniform beams.These methods are proved to be correct by instances and be valuable for the engineering practice and theoretical research.