To investigate the influence of end friction on compressive strength with different specimen shapes, we present a three-dimensional particle element approach for concrete, a series of numerical uniaxial compressive tests for standard cube specimen and standard cylinder specimen are conducted. The material properties are assumed to conform to the Weibull distribution law in consideration of its heterogeneity, and a method of parameter inversion calculation is used to get the mesoscopic mechanics parameters based on the material mechanics parameters. The results show that the end friction influences the peak strength, deformation character and failure mode of different geometries of concrete specimen. Shape effect increases as the friction coefficient between the platens of the testing machine and the concrete specimen increases; and the conversion ratio between cylinder and cube strength approaches 0.795 without any friction-reducing measure (f=0.6). The simulation results accord well with the codes, which shows the feasibility and effectiveness of the method.