We address the problem of optimizing resource sharing and flow control in a multiple spot-beam broadband satellite system that supports both unicast and multicast flows. Satellite communication systems, with their wide-area coverage and ubiquitous access to large number of users, clearly have an inherent advantage in supporting distributed applications that require concurrent transmission of content to multiple users. In order to remain competitive against other broadband technologies, next generation satellite systems will be required to support both unicast and multicast flows and offer optimal sharing of system resources between these flows. We show that a high load variation across the spot-beam queues may significantly under-utilize the system and be perceived unsatisfactory by potential users when both unicast and multicast flows are active in the system. We propose an optimization based-approach to balance the load in the system and conclude that it is possible to increase the average session rates of all active flows by up to 30% after this optimization is applied.