Multiprocessor platforms have been widely adopted in both embedded and server systems. In addition to the performance improvement, multiprocessor systems could have the flexibility in tolerating processor failures via task replication. This paper considers the replication of periodic hard real-time tasks in identical multiprocessor environments. Each task is replicated on K distinct processors, where K is a user-determined integer for fault tolerance to improve system reliability. When the objective is to minimize the maximum utilization in a system with a specified number of processors, we present a greedy algorithm with a 2-approximation ratio, and a polynomial-time approximation scheme is developed. For the minimization of the number of processors required to derive feasible schedules with task replication, we develop greedy algorithms with a 2- approximation ratio and an asymptotic polynomial-time approximation scheme.