As dcvicc technologies such as VLSI and Multichip Module (MCM) become mature, and larger and denser memory ICs arc implemented for high-performancc digital systems, power dissipation becomes a critical factor and can no longer be ignored cither in normal operation of the system or under test conditions. One of the major considerations in test scheduling is the fact that heat dissipated during test application is significantly higher than during normal operation (sometimes 100 - 200% higher). Therefore, this is one of the recent major considerations in test scheduling. Test scheduling is strongly related to test concurrency. Test concurrency is a design property which strongly impacts testability and power dissipation. To satisfy high fault coverage goals with reduced test application time under certain power dissipation constraints, the testing of all components on the system should be performed m parallel to the greatest extent possible. Some theoretical analysis of this problem has been carried out, but only at IC level. The problem was basically described as a compatible test clustering, where the compatibility among tests was given by test resource and power dissipation conflicts at the same time. From an implementation point of view this problem was identified as an Non-Polynomial (NP) complete problem In this thesis, an efficient scheme for overlaying the block-tcsts, called the extended tree growing technique, is proposed together with classical scheduling algorithms to search for power-constrained blocktest scheduling (PTS) profiles m a polynomial time Classical algorithms like listbased scheduling and distribution-graph based scheduling arc employed to tackle at high level the PTS problem. This approach exploits test parallelism under power constraints. This is achieved by overlaying the block-tcst intervals of compatible subcircuits to test as many of them as possible concurrently so that the maximum accumulated power dissipation is balanced and does not exceed the given limit. The test scheduling discipline assumed here is the partitioned testing with run to completion. A constant additive model is employed for power dissipation analysis and estimation throughout the algorithm.