Many examples of solar activity, such as large two-ribbon flares and prominence eruptions, are widely believed to involve the fast reconnection of magnetic flux tubes. Because of the difficulties associated with calculating the evolution of three-dimensional (3-D) flux tubes, however, the details of the energy-release process are poorly understood. In this paper we describe our first attempts to shed light on this important process. We describe the results of 3-D numerical simulations of initially distinct magnetic flux tubes interacting via magnetic reconnection. As a typical case, we consider an initial magnetic field given by a compact support function distribution so that the initial topology consists of two antiparallel flux tubes. We then impose an initial velocity field on this system which causes the flux tubes to move toward each other. As a result of this initial velocity, the tubes first flatten against each other and an electric current sheet begins to develop at the interface between them. After approximately 10 Alfven times we observe a burst of reconnection. The turbulent kinetic energy rises dramatically as two reconnection jets form, which are aligned parallel to the initial field. The reconnection phase lasts for approximately 20 Alfven times, by which time the central region of the initial tubes has been completely dissipated so that the system now consists of four tubes that are relatively widely separated and hence stop interacting. We find that the excitation of small-scale spatial structure in the flow field depends critically on the value of the Lundquist numbers. Compressible effects are insignificant for this particular case of flux tube reconnection. The numerical simulations are carried out using a three-dimensional explicit Fourier collocation algorithm for solving the viscoresistive equations of compressible magnetohydrodynamics. We also report on the performance of a new parallelized version of the code. ¿ American Geophysical Union 1995