The potential for the field-reversed configuration (FRC) as a fusion reactor concept, in particular as a candidate for an alternate concept device, depends on its confinement characteristics. The advantages of an FRC plasma are that it is easily produced and has low impurity concentrations. Currently, the electron and heat loss rates are higher than those predicted by Coulomb collisions. Analyses using the local approximation predict that LHD waves should exist near the separatrix, but experiments have failed to detect them. This local approximation may not be valid in two regions: near the field null, where ion orbits may be large and near the separatrix, where the equilibrium magnetic field and the plasma density can change appreciably. In this papaer we develop a method to analyze the stability of a 1-D FRC that takes the sharp gradients near the separatrix and the effect of the field null into account. This finite element code seeks a solution to the linearized Maxwell-Vlasov equations in the form of eigenvalues to a dispersion matrix. The dispersion matrix contains all the information pertaining to the stability of the plasma.