Phase sensitive techniques in scanning acoustical microscopy (SAM) yield information on surface height, film thickness, and other sample attributes that is not easily obtained from amplitude imaging alone. The process of unwrapping to obtain the spatial dependence of the attribute from a phase image breaks down in the vicinity of singular points where the complex signal vanishes and the phase is indeterminate. In a circuit around a phase singularity the phase changes by 2π or −2π. This paper discusses a number of models which demonstrate how phase singularities can arise in SAM, and measured reflection and transmission SAM images containing phase singularities are presented.