GYRE is an open-source stellar oscillation code, which calculates wave frequencies and functions for the (unforced) natural modes of an input stellar model. The code capabilities have recently been extended to encompass forced oscillations, so that the interior perturbations of a star caused by the gravitational field of a companion can be calculated. The standard approach to simulating tides involves parameterized equations that approximate how tides modify a binary orbit. However, this approach usually underestimates the circularization rate and overestimates the orbital shrinking rate. Our extended code, GYRE-tides, doesn't suffer these limitations, because it undertakes a full numerical solution of the tidal equations without approximations; therefore, it can better help us to analyze and interpret observations of binary systems. GYRE-tides is a couple of orders of magnitude faster than CAFein (the only other publicly available forced oscillation code), and can be widely applied to modeling the orbital evolution of close binaries hosting intermediate- and high-mass stars. Example applications of GYRE-tides to the heartbeat system KOI-54, and to a 5/2.5 Msun zero-age main-sequence binary, are presented and discussed.