In thermal recovery from unconsolidated oilsands reservoirs and in association with fluid mobility, formation compressibility and modulus of elasticity are closely related to pressure transient and stress redistribution behavior, which can collectively affect the steam chamber development. The non-linearity and stress-dependency in bulk compressibility and modulus of elasticity of rocks has been captured through the development of elegant constitutive models (e.g. nonlinear elastic hyperbolic model) and has been readily integrated into coupled reservoir-geomechanical simulation packages. To assess the significance of these nonlinearities for reservoirs with different initial stress states, this paper presents an analytical study where the associated impacts on the redistribution of stress (stress-paths) and the onset of geomechanical mobilization (shear dilation) under the assumption of uniaxial deformation are quantified. Within the scope of this paper, (semi-) analytical modeling is conducted while special attention has been devoted to (1) the vast range of depths of the existing oilsands reservoirs and the associated implications on the initial stress distribution as well as stress redistribution due to steam/water injection, (2) the impacts on the onset of geomechanical mobilization within the practical ranges of injection pressures, and (3) the evaluation of geomechanical mobilization potential for thermal (steam injection) versus non-thermal (cold water injection) pressurization. The results show that (1) the potential impact of stress dependency on the variability of the geomechanical properties (modulus of elasticity, Poisson's ratio and formation compressibility) is more significant for shallow reservoirs as compared to mid-depth and deep reservoirs, (2) the injection pressure required to onset the geomechanical mobilization may be under/overestimated if the non-linearity in the mechanical properties is overlooked, and (3) the thermal geomechanical mobilization (steam injection) may have a higher potential within practical ranges of operating pressures as compared to non-thermal techniques (cold water injection), especially for shallower reservoirs. The inherent limitations of the analytical workflows as well as the requirements of supporting efforts through coupled reservoir-geomechanical simulations are also discussed.