HyPA is a formalism that is suitable for the algebraic analysis of hybrid systems, i.e., systems with continuous (physical) as well as discrete (computational) components. Linearization is a useful first step in this analysis, because it reduces the complexity of model descriptions by transforming them into so-called linear form. We present an algorithm for the linearization of hybrid processes modeled in a subset of hybrid process algebra (HyPA) and prove its correctness. This algorithm is able to linearize most HyPA constructs, except recursive parallelism, the empty process, and disrupts that are not a flow prefix. We also extend HyPA with an abstraction operator, which is used in the linearization algorithm.