A number of mathematical programming models for test construction have been presented in recent years. For example, Adema & van der Linden (1989) developed models for maximizing test reliability, and van der Linden & Boekkooi-Timmninga (1988) developed models for the construction of parallel tests. A minimization and a maximization model for parallel test construction under constraints are pre-sented here. The purpose of the minimization model is to construct weakly and strongly parallel testsa of minimum length. The purpose of the maximization model is to construct weakly and strongly parallel tests with maximum test reliability.