An approximation technique for locating the surface- and leaky-wave poles for a lossy dielectric slab is presented. The problem is reduced to the simultaneous solution of two transcendental equations (for each of the perfect magnetic conductor (PMC) and perfect electric conductor (PEC) cases) which is shown to yield a simple approximate solution for the poles, and which can subsequently be refined using numerical optimization. The technique yields both surface-wave and leaky-wave poles, and results are presented for a typical example to demonstrate the approach. The greatest approximation accuracy was observed for surface-wave and leaky-wave poles well removed from the spectral gap. For poles either within or in close proximity to the spectral gap, an alternative iterative technique is proposed. Expressions for the number of proper plus improper surface-wave poles in a given problem are also derived.