A conceptual model is proposed for the short-term operation of subduction-accretion systems at convergent margins. The operation is described in terms of the mass fluxes among the four system components, namely, the accretionary (or prowedge) wedge (P), an uplifted plug (U), a retrowedge (R), and the subduction zone. The latter consists of a conduit (C) of slowly moving and deforming material and an underlying subduction channel where material moves and deforms more rapidly. A broad range of convergent margin types can be accommodated within the conceptual model framework, with differing short-term modes that depend on which of the P-U-R-C components that are active. Finite element geodynamical model experiments are used to investigate whether these modes are dynamically feasible. These experiments determine excitation of modes under controls that include model entry and exit mass fluxes; flexural loading by accreted material and slab pull forces; boundary velocities corresponding to subduction and subduction zone advance/retreat; distribution, thickness, and density of accreted sediment; and internal frictional properties of the Coulomb sediments. That all modes, with the exception of P (in which only a prowedge is created), are seen in the models provides support for the concepts and allows conditions that favor particular modes to be recognized. In addition, the finite deformation predicted by the models is used to infer the long-term tectonic styles associated with both single-mode evolutions and those that exhibit mode switching. A steady state mass balance can occur for modes 0 (pure subduction), P-C (i.e., where components P and C are active), or other modes when the surface mass denudation plus the subduction flux balances accretion plus tectonic underplating. The P-C mode is favored by subduction zone retreat and/or an increasing subduction load and creates an apparent landward dipping backstop. P-U-C is predicted to be the most common mode, and it creates an apparent seaward dipping backstop. P-U-R-C is an inefficient mode but is favored by easily detached retrocrust or sediment and/or a decreasing subduction load.