In this paper, an extension of Modelica, entitled Optimica, is presented. Optimica extends Modelica with language constructs that enable formulation of dynamic optimization problems based on Modelica models. There are several important design problems that can be addressed by means of dynamic optimization, in a wide range of domains. Examples include, minimum-time problems, parameter estimation problems, and on-line optimization control strategies. The Optimica extension is supported by a prototype compiler, the Optimica compiler, which has been used successfully in case studies.