Partition function or Fisher zeros play a fundamental role in the theory of phase transitions in classical lattice statistical mechanics. In this talk I will present some results on the properties of partition and generating function zeros in a model of an adsorbing self-avoiding walk. I will show how to approximately enumerate self-avoiding walks and present numerical results on the location of partition and generating function zeros. Theorems constraining the distribution of zeros in the complex plane, based on the distribution of polynomial zeros, will also be discussed. These results show that partition function zeros are constrained to be located in annular regions with center at the origin in the complex plane.