The one‐dimensional phenomena which occur when shock‐induced flows in ideal gases interact with transverse magnetic fields of finite extent are analyzed from both the steady‐state and transient viewpoints. The steady‐state analysis assumes steady flow exists within the interaction zone. It is shown that there are four types of interactions. These involve the presence or absence of standing or upstream‐propagating reflected shock waves, and rarefaction waves on the downstream side of the interaction zone. The types of interactions are functions of the initial Mach number of the shock‐induced flow, the interaction parameter, the magnetic Reynolds number, and the amount of electrical energy withdrawn from the flow. The method of characteristics is used to analyze transient phenomena. The transient problem is described by a five‐characteristic network, which is reduced to four characteristic directions when the flow velocity is small compared to the electromagnetic signal velocity. The transient analysis can be used to determine the position where the reflected shock wave forms and the length of time required for the flow within the interaction zone to approach steady‐state conditions.