Robot-assisted dressing offers an opportunity to benefit the lives of many people with disabilities, such as some older adults. However, robots currently lack common sense about the physical implications of their actions on people. The physical implications of dressing are complicated by non-rigid garments, which can result in a robot indirectly applying high forces to a person’s body. We present a deep recurrent model that, when given a proposed action by the robot, predicts the forces a garment will apply to a person’s body. We also show that a robot can provide better dressing assistance by using this model with model predictive control. The predictions made by our model only use haptic and kinematic observations from the robot’s end effector, which are readily attainable. Collecting training data from real world physical human-robot interaction can be time consuming, costly, and put people at risk. Instead, we train our predictive model using data collected in an entirely self-supervised fashion from a physics-based simulation. We evaluated our approach with a PR2 robot that attempted to pull a hospital gown onto the arms of 10 human participants. With a 0.2s prediction horizon, our controller succeeded at high rates and lowered applied force while navigating the garment around a persons fist and elbow without getting caught. Shorter prediction horizons resulted in significantly reduced performance with the sleeve catching on the participants’ fists and elbows, demonstrating the value of our model’s predictions. These behaviors of mitigating catches emerged from our deep predictive model and the controller objective function, which primarily penalizes high forces.