The compressive strength of masonry, whether brick or concrete block masonry is an important parameter in the design of masonry structure. The compressive strength of masonry depends on many parameters including strength and modulus of elasticity of the unit and mortar. Experimental determination of compressive strength of masonry is time consuming, labour intensive and expensive. The numerical and analytical approach is an effective alternative to experimental investigations. This work aims to simulate the behaviour of block masonry under compression using ABAQUS and ANSYS software. The results obtained from the experimental investigation are used as input to carry out numerical analysis in the above-mentioned software. The results obtained from each of these software are in line with the experimental findings and is promising.