This study elucidates the concept of material forces at the tip of an evolving crack in brittle homogeneous materials by using a numerical lattice approach. A 2D lattice with an erosion algorithm is employed in the context of LEFM to investigate two well-known classic fracture problems in Mode I, i.e., a center-cracked rectangular panel with finite dimensions and a three-point bending beam with a notch. Validated by the well-developed analytical solutions for these two configurations, the lattice is used to derive crack tip driving forces in the direction of crack propagation based on the change of global stiffness matrix of the mesh before and after crack growth without any stress calculations, and to obtain the material forces opposing the tip motion utilizing the Eshelby-stress tensor and local force balance law in cracked bodies. Comparing these two distinct approaches, it is observed that the discrete material forces at the crack tip are closely equal to the tip driving forces, but with different signs, confirming that the lattice approach approximates the values of crack tip material forces using Eshelby-stress distributions. Moreover, satisfying C1 continuity by including rotational displacements for the Euler–Bernoulli based frame struts, there is no need for the lattice model to update interior computational point positions in the mesh to eliminate spurious material forces away from the tip, a complication observed in Finite Element formulations. The discrete material forces are then characterized for the two problems by only three material parameters, i.e., Young's modulus, uniaxial tensile strength, and the configurational characteristic width or crack band. After conducting a regression analysis on the material forces with respect to different tensile strength values, a parabolic relationship emerges between the material forces and tensile strengths. This feature is employed to extract the crack band width values by the lattice approach, which are explicitly used to obtain the crack tip material forces of the two classic problems. Being simple in terms of constitutive formulation, failure criterion, and capable of obtaining the configurational characteristic width or crack band for different boundary value problems for brittle homogeneous isotropic materials, the numerical lattice formulation sheds light on the important concept of material force in Configurational and Fracture Mechanics.