We consider the positive solutions to a class of nonlinear fourth-order two-point boundary value problems

where the nonlinear term is allowed to be singular.Main foundation is the approximation theorem of completely continuous operators and the Guo-Krasnosel’skii fixed point theorem of cone expansion-compression type.In mechanics

this class of problems describe the deformation of an elastic beam rigidly fixed at both ends.In order to describe the growth of nonlinear term we introduce the principal and singular parts of nonlinear term.The results show that this class of problems can have n positive solutions provided the heights of principal part and the integrations of height function on some bounded sets are appropriate

where n is an arbitrary positive integer.