Six types of numerical specimens containing two notches are set up to numerically investigate the effect of element size on rock shear strength and failure pattern using RFPA2D (rock failure process analysis) code. These specimens are of the same geometrical dimension 180 mm×180 mm and have been discretized into 61×61, 122×122, 183×183, 244×244, 305×305, and 366×366 elements.The width of notches is about 2.95 (180/61) mm and the length is 45mm. The specimens are placed in a direct shear box. A lateral confining pressure with a value of 0.15MPa is invariably loaded in the vertical direction and an increasing horizontal displacement with 0.002mm/step is applied in the horizontal direction. The whole shear failure progress and associated stress field for the specimens are visually represented. Results show that the crack propagation is mostly influenced by the stress field in the vicinity of the notch tip, the required element size would be necessary in order to obtain good results. In general, for a coarse mesh, the stress field close to the notch tip can’t be represented accurately and shear strength obtained by such discretisation is slightly higher than the accurate value. For a fine mesh, the notch tip spreads through a relatively large number of elements and the stress field in vicinity of notch tip is well represented by the finite element approximation, therefore the failure pattern is consistent with real physical fracture mode.