A theoretical model to predict continuous deformation and acceleration of spherical or cylindrical metallic casings driven by detonation products inwards or outwards before fracture occurring is proposed in this paper. The casing materials are assumed to be rigid viscoplastic medium and the geometries are one dimension i.e., the explosive charge is initiated at the spherical center or on the cylindrical axis in the divergent case, or uniformly on the explosive shell's outer surface in the convergent case. The acceleration movements of spherical and cylindrical casings calculated with this model are in good agreement with experimental and numerical results performed with the finite element hydrocode DYNA2D. It is concluded that this model describes well one-dimensional divergent and convergent movements of spherical or cylindrical casings under explosive loading, and provides a useful method to explore related problems, such as shell's fragmentation, its maximum velocity before fracture, blast wave in the near area adjacent, to the casing and solid liner implosion.