The objective of the paper is to determine the stable mechanical equilibrium states of an oblate capsule subjected to a simple shear flow, by positioning its revolution axis initially off the shear plane. We consider an oblate capsule with a strain-hardening membrane and investigate the influence of the initial orientation, capsule aspect ratio $a/b$ , viscosity ratio ${\it\lambda}$ between the internal and external fluids and the capillary number $Ca$ which compares the viscous to the elastic forces. A numerical model coupling the finite element and boundary integral methods is used to solve the three-dimensional fluid–structure interaction problem. For any initial orientation, the capsule converges towards the same mechanical equilibrium state, which is only a function of the capillary number and viscosity ratio. For $a/b=0.5$ , only four regimes are stable when ${\it\lambda}=1$ : tumbling and swinging in the low and medium $Ca$ range ( $Ca\lesssim 1$ ), regimes for which the capsule revolution axis is contained within the shear plane; then wobbling during which the capsule experiences precession around the vorticity axis; and finally rolling along the vorticity axis at high capillary numbers. When ${\it\lambda}$ is increased, the tumbling-to-swinging transition occurs for higher $Ca$ ; the wobbling regime takes place at lower $Ca$ values and within a narrower $Ca$ range. For ${\it\lambda}\gtrsim 3$ , the swinging regime completely disappears, which indicates that the stable equilibrium states are mainly the tumbling and rolling regimes at higher viscosity ratios. We finally show that the $Ca$ – ${\it\lambda}$ phase diagram is qualitatively similar for higher aspect ratio. Only the $Ca$ -range over which wobbling is stable increases with $a/b$ , restricting the stability ranges of in- and out-of-plane motions, although this phenomenon is mainly visible for viscosity ratios larger than 1.