Viscous flow and deformation of a Newtonian fluid between rigid boundaries have been modeled for investigating deformation of a forearc wedge and a regional metamorphic belt as a weak deforming zone between the plates at convergent boundaries. Three types of analytic formulations together with numerical formulations for a Newtonian fluid with a constant viscosity are used for investigating various flows and deformation: (1) flows induced by squeezing between two parallel boundaries, (2) flows induced by squeezing and heterogeneous mass influx in the wedge between two oblique boundaries (e.g., accretionary wedge over the subducting plate with the continental plate as a backstop), and (3) flows induced by dragging along the boundaries and by homogeneous mass influx in the wedge as in type 2. All cases include strike-slip movements of the boundaries, which allows us to investigate three-dimensional (3-D) deformation (e.g., 3-D corner flow). The corresponding flow, deformation of infinitesimal and finite elements, and the timescale of flow are calculated for each configuration with various mechanical boundary conditions. The model results show that configuration and mechanism of the flow can be inferred from the spatial variation of finite deformation (e.g., deformed radiolarians as a strain marker and geometry of folding as finite deformation of a large block). In particular, prolate strain nearly parallel to the strike of subduction zone, together with a large-scale folding, can be a good indicator for deformation in the forearc wedge associated with 3-D corner flow induced by oblique subduction. Deformation observed in the Cretaceous regional metamorphic belts in southwest Japan can be explained by this mechanism.