Circulating monocytes are recruited to the tumor microenvironment, where they can differentiate into macrophages that mediate tumor progression. To reach the tumor microenvironment, monocytes must first extravasate and migrate through the type-1 collagen rich stromal matrix. The viscoelastic stromal matrix around tumors not only stiffens relative to normal stromal matrix, but often exhibits enhanced viscous characteristics, as indicated by a higher loss tangent or faster stress relaxation rate. Here, we studied how changes in matrix stiffness and viscoelasticity impact the three-dimensional (3D) migration of monocytes through stromal-like matrices. Interpenetrating networks of type-1 collagen and alginate, which enable independent tunability of stiffness and stress relaxation over physiologically relevant ranges, were used as confining matrices for 3D culture of monocytes. Increased stiffness and faster stress relaxation independently enhanced the 3D migration of monocytes. Migrating monocytes have an ellipsoidal or rounded wedge-like morphology, reminiscent of amoeboid migration, with accumulation of actin at the trailing edge. Matrix adhesions were dispensable for monocyte migration in 3D, but migration did require actin polymerization and myosin contractility. Mechanistic studies indicate that actin polymerization at the leading edge generates protrusive forces that open a path for the monocytes to migrate through in the confining viscoelastic matrices. Taken together, our findings implicate matrix stiffness and stress relaxation as key mediators of monocyte migration and reveal how monocytes use pushing forces at the leading edge mediated by actin polymerization to generate migration paths in confining viscoelastic matrices.