The detailed analytical procedure to predict the parameters, such as load-crack mouth opening displacement and load-load line displacement responses, required to characterize the concrete fracture phenomenon is investigated. The present work involves numerical modeling of geometrically similar three point bend (TPB) beams having constant length to depth ratio. The simulation of TPB specimen yields the load-load line displacement and load-crack mouth opening displacement response of the beam, which characterize the concrete fracture phenomenon. The numerically observed response is found to be in excellent agreement in most of the cases with the reported literature. Based on the completeness of interpolation function, the superiority of constant strain triangle (CST) elements over the quadratic rectangle element is explained and proved by considering the benchmark problems. A number of computational studies are performed by incorporating the fracture based softening model to establish the mesh sensitivity. Keywords: Concrete fracture, Mesh sensitivity, CST, Quadratic element.