Temperature and pressure changes associated with the cyclic steam stimulation (CSS) used in heavy oil production from sands are accompanied by significant deformation. Inversion of induced reservoir pore-pressure changes from deformation measurements may provide a potentially powerful reservoir-monitoring tool if the issues of measurement noise, uncertainty in model parameterization, and numerical accuracy and stability can be resolved. We discuss inverting injection-induced reservoir pressure changes from observable surface deformations using a linear poroelastostatic model of a heavy oil reservoir. We also present results of inversion from surface tilt measurements taken at a production site undergoing CSS. We demonstrate that a stable inversion of the reservoir pore-pressure change can be achieved from sparse and noisy surface tilt measurements using constrained regularized optimization. The results provide an insight into the heterogeneity of reservoir stimulation and could help with optimizing well locations and stimulation protocols.