Abstract : We rely on the lattice element method to simulate and analyze the stress fields at subparticle scales in two-dimensional granular solids composed of particles of variable stiffness together with an interstitial matrix of variable volume fraction. We find that the contact force distributions as approached from the subscale stresses are similar to those obtained from a particle-scale discrete element approach. This means that the well-known properties of force distributions in model granular media, with hard particles and without an interstitial phase, can be extended to materials such as concrete and sandstone involving a jammed particle phase. Interestingly, the stress distributions are exponential at the contact zones and they are mainly guided by the particle phase in compression and by the matrix in tension. We also show that the distributions are increasingly broader for a decreasing matrix volume fraction in tension whereas in compression they depend only on the particle stiffness.