We are concerned with user selection and resource allocation in wireless networks for semi-elastic applications such as video conferencing. While many packet scheduling algorithms have been proposed for elastic applications, and many user selection algorithms have been proposed for inelastic applications, little is known about optimal user selection and resource allocation for semi-elastic applications in wireless networks. We consider user selection and allocation of downlink transmission power and subcarriers in an orthogonal frequency division multiplexing cellular system. We pose a utility maximization problem, but find that direct solution is computationally intractable. We first propose a method that makes joint decisions about user selection and resource allocation by transforming the utility function into a concave function so that convex optimization techniques can be used, resulting in a complexity polynomial in the number of users with a bounded duality gap. This method can be implemented if the network communicates a shadow price for power to power allocation modules, which in turn communicate shadow prices for rate to individual users. We then propose a method that makes separate decisions about user selection and resource allocation, resulting in a complexity linear in the number of users.