Constitutive equations for fresh mortar and fresh concrete provide the characterization of the mixture’s flow and the quantification of the rheological properties. This paper presents a constitutive material model for mortar and concrete that builds on previous research. It postulates that (a) the shear stress is the sum of three components: static interaction between particles, dynamic interaction between particles, and collision of particles; and (b) the cell is a representative volume of the mixture. For fresh concrete, the effects of particle collisions are negligible due to high concentration, and the equation reduces to the Bingham model. Experimental data reported in the literature was employed to evaluate the predictive capabilities of the constitutive equations. The model results are found to compare very well with the measured experimental data and the difference is within the measurement errors.