We expand the theory of critically tapered Coulomb wedge for accretionary prisms by considering stress changes in subduction earthquake cycles. Building on the Coulomb plasticity of the classical theory, we assume an elastic--perfectly Coulomb plastic rheology and derive exact stress solutions for stable and critical wedges. The new theory postulates that the actively deforming, most seaward part of an accretionary prism (the outer wedge) overlies the updip velocity-strengthening part of the subduction fault, and the less deformed inner wedge overlies the velocity-weakening part (the seismogenic zone). During great earthquakes, the outer wedge is pushed into a compressively critical state, with an increase in basal and internal stresses and pore fluid pressure. After the earthquake, the outer wedge returns to a stable state. The outer wedge geometry is controlled by the peak stress of the updip velocity-strengthening part of the subduction fault achieved in largest earthquakes. The inner wedge generally stays in the stable regime throughout earthquake cycles, acting as an apparent backstop and providing a stable environment for the formation of forearc basins. The new theory has important implications for the studies of the updip limit of the seismogenic zone, the evolution of accretionary prisms and forearc basins, activation of splay faults and tsunami generation, evolution of the fluid regime, and mechanics of frontal prisms at margins dominated by tectonic erosion.