Speech processing refers to a set of tasks that involve speech analysis and synthesis. Most speech processing algorithms model a subset of speech parameters of interest and blur the rest using signal processing techniques and feature extraction. However, evidence shows that many speech parameters can be more accurately estimated if they are modeled jointly; speech synthesis also benefits from joint modeling.This thesis proposes a probabilistic generative model for speech called the Probabilistic Acoustic Tube (PAT). The highlights of the model are threefold. First, it is among the very first works to build a complete probabilistic model for speech. Second, it has a well-designed model for the phase spectrum of speech, which has been hard to model and often neglected. Third, it models the AM-FM effects in speech, which are perceptually significant but often ignored in frame-based speech processing algorithms. Experiment shows that the proposed model has good potential for a number of speech processing tasks.