This paper introduces VibPress, a software technique that enables pressure input interaction on mobile devices by measuring the level of vibration absorption with the built-in accelerometer when the device is in contact with a damping surface (e.g., user's hands). This is achieved using a real-time estimation algorithm running on the device. Through a user evaluation, we provide evidence that this system is faster than previous software-based approaches, and accurate as hardware-augmented approaches (up to 99.7% accuracy). With this work, we also provide an insight about the maximum number of pressure levels that users can reliably distinguish, reporting usability metrics (time, errors and cognitive load) for different pressure levels and types of gripping gestures (press and squeeze).