The phase problem of X-ray crystallography is well-known and a number of methods have been developed to solve it. The discovery of invariants and semi-invariants is almost always the first step in the solution and triplet invariants have proved extremely useful. In this work we present a fast parallel method for triplet generation that works for moderate-sized proteins. Variations of the algorithm and implementations for two popular models of parallel computation, SIMD and SPMD, are described. Performance results are given for implementations on the MasPar MP-1 and two networks of workstations (NoWs). Nearly linear scalability is achieved and the method has been used for structures involving more than 3000 reflections and more than 8 million triplets.