Classical process algebras, such as CCS, are qualitative in that they do not consider time or other quantities explicitly. PEPA, developed by Hillston, is quantitative with stochastic semantics given in terms of continuous time Markov chains, or with continuous deterministic semantics given in terms of ordinary differential equations (ODEs). Process algebras have also been proposed with hybrid semantics consisting of both discrete and continuous behaviour. In this talk, I will describe our process algebra, which is both stochastic and hybrid. Stochastic HYPE is highly compositional when dealing with continuous aspects of the model, and this distinguishes it from previous hybrid process algebras. Its semantics are given in terms of transition-driven stochastic hybrid automata, a subset of piecewise deterministic Markov processes. We have a simple technique to determine which stochastic HYPE models are well-behaved. Bisimulation is defined at two different levels, and the relationship between these equivalences will be examined. Application of stochastic HYPE to model real world systems will be presented, including, time permitting, a ZebraNet model developed by Cheng Feng in his MSc dissertation. This is joint work with Jane Hillston and Luca Bortolussi.