Solid- and liquid-wall reactors are now under consideration as pellet fusion reactor systems. A thermal shock problem induced by a deposition of soft x rays may be more serious to the solid-wall reactor system than to the liquid-wall reactor system. The engineering feasibility of the solid-wall reactor system is assessed by means of analytical solutions of the thermomechanical dynamics associated with a sudden and uniform temperature rise, and of finite element solutions of the reactor dynamics associated with the surface heating due to the deposition of soft x rays. Fatigue damage caused by the thermal shock would limit the pulsed pellet gain to a small value compared to that of a conceptual design proposed recently. Graphite has the highest allowable temperature in comparison with such alternative materials as stainless steel, niobium, and molybdenum. However, the allowable pellet gain per microexplosion may be 2.2 MJ even if the graphite is used for the coating or wall material of a spherical reactor of 5-m radius.