Three-dimensional hydrodynamic simulations of cosmic jets interacting with their environment in a manner which could deflect them have been made. Specifically, off-center collisions of jets with dense clouds of gas have been examined, together with the ram pressure deflection of jets caused by motion of the jet source through a gaseous medium. In the case of jet-cloud interactions, it is found that deflection of the jet in a coherent manner is not very effective, even with an optimum geometry for the collision. There are two reasons for this result; first, the major effect of the collision at early epochs is to drastically decelerate the jet to velocities less than one tenth the original value, and second, at later epochs (> 10(7) yr) the cloud is destroyed by the jet. These effects do not produce a geometry which is consistent with observations of bending in cosmic jets. It is possible, however, that such an encounter could produce double hot spots in the extremities of strong radio sources. In the case of jet-wind interactions, ram pressure deflection is found to be more effective than previously supposed. This occurs because the full three-dimensional calculation includes the momentum transfer along the jet boundary which has been omitted from previous analytic approximations.