It has become increasingly common for companies to offer make-to-stock (MTS) and make-to-order (MTO) versions of the same product through different sales channels. To satisfy these two distinct demand streams, one strategy is to produce both the MTS and MTO items in a single “hybrid” facility partially comprised of flexible servers or machines. We develop a multi-server queueing model of this system, where a subset of the servers or machines is dynamically switched between MTS and MTO production via a congestion-based switching policy. We develop analytical formulae for quantifying all major performance measures of the system. We also present a search procedure to find the capacity and inventory control parameters which minimize the total costs of the system while satisfying the customer service constraints. Numerical results are used to illustrate the general behavior of the dynamic hybrid system and to compare its performance to that of a more conventional static hybrid facility with dedicated MTS and MTO servers. For high levels of traffic intensity, the dynamic system is shown to provide superior customer service for both sales channels with lower finished goods inventory levels.