In this paper we develop a demand system approach for estimating preferences for an arbitrarily large set of quality differentiated goods at the individual or household level. We apply the model to an outdoor recreation data set consisting of day trips to 62 beaches in the Mid- Atlantic region and analyze the welfare effects of changes in beach characteristics and availability. Interest in the value of beach recreation opportunities arises from policy makers' need to assess the merits of beach nourishment programs and to measure the damages resulting from acute environmental accidents that impact beach availability. The Hicksian consumer surplus estimates reported in this paper address these issues and represent the first welfare measures derived from a theoretically consistent demand system model that accounts for interior and corner solutions and accommodates a large set of quality differentiated goods.