Composition-dependent stress fields in continuous and mechanically isolated material can, it is shown, initiate and maintain conversion of chemical to kinetic energy. Though the process is analogous to natural convection, neither the body force of the well-known buoyancy mechanism nor the singular inhomogeneity and anisotropy of the interfacial tension mechanism is required. In the cases examined, the material is represented by the constitutive relation for incompressible Newtonian fluid augmented by an active stress which must be anisotropic or nonlinear in concentration gradients (or other, equivalent gradients) in accordance with the oft-misquoted Curie principle. The concentration gradients are supposed to be sustained by steady chemical reaction (or an equivalent transformation process) throughout the material and by exchange with surroundings. Conventional linear analysis of asymptotic stability is used to identify types of stress/concentration-gradient coupling that can render a quiescent state of reaction and diffusion unstable when concentration gradients exceed critical values. It is found that both deviatoric (pure shear) and antisymmetric active stress can support two-dimensional convective instability in a cylinder of material in which the quiescent state is circularly symmetric. Certain cases of stationary instability are solved exactly. Others involving both stationary and oscillatory instability are treated by a new version of the Galerkin method. The results establish the possibility of generating fluid motion by mechanochemical means in continuous material having appropriate subcontinuum structure. Whatever their relevance to protoplasmic movement in biological systems they do contain challenges for experimental and theoretical fluid mechanics and related areas of rheology and chemistry.