This paper presents a semi-automated method to compute matrix elements at the Leading Order and the Next-to-Leading Order in the ABC model of particle physics. The ABC model consists of three scalar particles and they interact only when all three particles are present in the interaction. In the Next-to-Leading Order calculations, one often has to deal with ultraviolet divergences. Some of the techniques such as Wick’s rotation, Feynman parameterisation, and dimensional regularization which are useful in Next-to-Leading Order computations are presented by applying them on the ABC model calculations and also implemented in python based programs using Computer Algebra System.