The paper deals with the problem \(u''+ g(t,u)= 0\), \(u(0)= u(1)= 0\), where the function \(g\) can be singular at \(t=0\), \(t=1\) and \(u=0\). The authors prove the existence of positive solution of this problem, supposing in the main that nonlinearity has to become large enough when \(u\) goes to zero and singularity has to be small enough so that the Green operator corresponding to BVP under consideration can be applied. The technique of proof uses essentially the method of upper and lower solutions and the results generalize some earlier papers by Taliaferro, Bobisud, Gatica, Zongming Guo, Janus and Myjak.