Previous mantle convection studies with continents have revealed a first-order influence of continents on mantle flow, as they affect convective wavelength and surface heat loss. In this study we present 3D spherical mantle convection models with self-consistent plate tectonics and a mobile, rheologically strong continent to gain insight into the effect of a lithospheric heterogeneity (continents vs. oceans) on plate-like behaviour. Model continents are simplified as Archaean cratons, which are thought to be mostly tectonically inactive since 2.5 Ga. Long-term stability of a craton can be achieved if viscosity and yield strength are sufficiently higher than for oceanic lithosphere, confirming results from previous 2D studies. Stable cratons affect the convective regime by thermal blanketing and stress focussing at the continental margins, which facilitates the formation of subduction zones by increasing convective stresses at the margins, which allows for plate tectonics at higher yield strength and leads to better agreement with the yield strength inferred from laboratory experiments. Depending on the lateral extent of the craton the critical strength can be increased by a factor of 2 compared to results with a homogeneous lithosphere. The resulting convective regime depends on the lateral extent of the craton and the thickness ratio of continental and oceanic lithosphere: for a given yield strength a larger ratio favours plate-like behaviour, while intermediate ratios tend towards an episodic and small ratios towards a stagnant lid regime.