People spend a substantial part of their lives at rest in bed. 3D human pose and shape estimation for this activity would have numerous beneficial applications, yet line-of-sight perception is complicated by occlusion from bedding. Pressure sensing mats are a promising alternative, but training data is challenging to collect at scale. We describe a physics-based method that simulates human bodies at rest in a bed with a pressure sensing mat, and present Pressure-Pose, a synthetic dataset with 206K pressure images with 3D human poses and shapes. We also present PressureNet, a deep learning model that estimates human pose and shape given a pressure image and gender. PressureNet incorporates a pressure map reconstruction (PMR) network that models pressure image generation to promote consistency between estimated 3D body models and pressure image input. In our evaluations, PressureNet performed well with real data from participants in diverse poses, even though it had only been trained with synthetic data. When we ablated the PMR network, performance dropped substantially.