This report describes a network mesh analysis technique which can be used to calculate transient or steady-state eddy current distributions on a conducting surface. In general, the surface may have any continuous three-dimensional shape, may vary in surface resistivity, and may include holes. The surface is divided into a network of branches for each of which are calculated a resistance, a self-inductance, and a set of mutual inductances to all other branches. The resulting branch resistance and branch inductance matrices are transformed into mesh matrices using a conventional network procedure. A set of simultaneous differential equations can then be established to solve for eddy currents. The set of equations is generally solved for a time series of eddy currents caused by an external source of excitation. Various initial conditions can be used to find other solutions of interest such as the self decay of an arbitrary current distribution. Great simplification is possible by imposing boundary conditions to take advantage of symmetry. In addition, the set of equations needs to be solved one time only for the special cases of pure inductance, pure resistance, or steady-state.