Proper treatment of selections is essential in parametric feature-based design. Data exchange is one of the most important operators in any design paradigm. In this paper we address two-dimensional selections (faces and surfaces) in feature-based data exchange (FBDE). We define the problem formally and present algorithms to address it, in general and in various cases in which feature rewrites are necessary. The general algorithm operates at a geometric level and does not require solving the persistent naming problem, which is required for selection support inside a single CAD system. All algorithms are applicable to the Universal Product Representation (UPR) FBDE architecture, and the general algorithm is also applicable to the STEP parametrics specification.