Modelling of concrete through 3 D constitutive material models is a challenging subject due to the numerous nonlinearities that occur during the monotonic and cyclic analysis of reinforced concrete structures. Additionally, the ultimate limit state modelling of plain concrete can lead to numerical instabilities given the lack of steel rebars that usually provide with the required tensile strength inducing numerical stability that is required during the nonlinear solution procedure. One of the commonly used 3 D concrete material models is that of the Kotsovos and Pavlovic, which until recently it was believed that when integrated with the smeared crack approach, it can only be used in combination with relatively larger in size finite elements. The objective of this study is to investigate into this misconception by developing different numerical models that foresee the use of fine meshes to simulate plain concrete and reinforced concrete specimens. For the needs of this research work, additional experiments were performed on cylindrical high strength concrete specimens that were used for additional validation purposes, whereas results on a reinforced concrete beam found in the international literature were used as well. A discussion on the numerical findings will be presented herein by comparing the different experimental data with the numerically predicted mechanical response of the under study concrete material model.