This talk will consider the stability of time independent solutions to the incompressible, inviscid Euler equations on the torus whose stream functions have the form ψ=U(ξ)=U(p1x+p2y) for fixed integers p1 and p2. By an appropriate change of coordinates and separation of variables, the linearised spectral problem is reduced to the study of a Hill's equation with a complex potential. By using Hill determinants, an Evans function of the original linearised Euler equation can be constructed. For certain, well-known shear flows, the form of the Hill determinant makes such an Evans function numerically straightforward to compute.