ABSTRACT. Concurrent program refinement algebra provides a suitable basis for supporting mechanised reasoning about shared-memory concurrent programs in a compositional manner, for example, it supports the rely/guarantee approach of Jones. The algebra makes use of a synchronous parallel operator motivated by Aczel’s trace model of concurrency and with similarities to Milner’s SCCS. This paper looks a defining a form of fairness within the program algebra. The encoding allows one to reason about the fair execution of a single process in isolation as well as define fair parallel in terms of base parallel operator, of which no fairness properties are assumed. An algebraic theory to support fairness and fair parallel is developed.