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This paper formulates the call admission control problem for media on demand (audio and video) requests in the form of a mathematical optimization model. This model allocates proper portions of the available capacity to the customers of various service classes in order to maximize service provider's revenue, resource utilization, and customer satisfaction. Upon receiving a media request, the provider decides (based on the estimated available bandwidth) whether to accept it in the requested class or to offer a service in another service class. A Markov chain model is employed to formulate admission control strategies, and the limiting probabilities are used to construct a revenue maximization formulation of the problem. We use both an analytical model and computer simulation to investigate effect of offer-based admission control for media services on providers' revenue and customer satisfaction measured by call rejection probability.