Fluid Flow Mechanics deals with flows which move due to internal particle pressure and pressure gradients. This paper attempts to derive a roughly parallel although an entirely different concept of a relatively unknown mathematical and yet potential physical process which the author refers to simply as Field Flow Mechanics and which deals with pressure gradients of a field created by a macroscopic and as yet unknown ‘generator’. The development of Field Flow Mechanics finds a natural exposition in transportation of the ‘generator’ across, for example, interstellar distances, i.e. space travel. These fields are obviously not yet in existence, but if they were, they and their gradients would be presumed to be macroscopic variables. This paper tries to anticipate their existence by predicting what would happen if they were in existence and even to use dimensional analysis in order to get some kind of grip on the possible reality of such fields. The approach is to try and derive from a set of geometric assumptions a Lagrangian structure such that the Euler-Lagrange equations of motion can be invoked. In the course of attempting to derive a geometric Lagrangian structure, several surprising results occur such as the derivation of an antisymmetric tensor which finds a convenient interpretation as a new type of ‘electromagnetic’ field which yields a ‘magnetic’ monopole feature in addition to a rotational feature. This paper also attempts to show how Field Flow Mechanics admits a non-linear partial differential equation of the Hamilton-Jacobi type which allows velocities in excess of the speed of light while allowing a parametric time interval on the ‘generator’ to equate with the coordinate time interval of the source planet in order to make interstellar travel a viable process.