Abstract A finite element method is developed to solve two-dimensional consolidation problems for composites manufacturing. The consolidation governing equations, one for solid stress and one for fluid pressure, are derived using a local volume averaging approach, and the two equations are strongly coupled. A special anisotropic, hyperelastic constitutive equation is developed for the solid stress. This equation matches Gutowski's model for consolidation transverse to the fibers, and has a high stiffness parallel to the fibers. An updated Lagrangian method is used to solve the equations, using implicit time integration and a successive substitution method. The code is applied to several case studies to explore two-dimensional consolidation effects. A free edge affects the thickness profile during consolidation, but the final thickness can still be uniform. This effect is substantial in the region close to the edge, and it propagates progressively from the edge toward the center. Simulations were also performed for laminates that bend to form a corner. The corner is thicker than the flat region after consolidation. Wiggles, similar to fiber buckling, arise at low values of shear modulus when using a male mold. Large values of the solid shear modulus cause the corner effect to extend far into the adjacent flat region. The length of the flat region also affects the consolidation of the corner.