In 1966, Coleman, Markovitz and Noll published a book entitled Viscometric Flows of Non-Newtonian Fluids. The analysis presented there is based on the concept of an incompressible simple fluid (simple liquid), which Walter Noll had introduced in 1958. About 5 years ago he introduced the concept of a simple semi-liquid. It turns out that the analysis given in the book mentioned above can be extended to simple semi-liquids. The behavior of simple liquids in viscometric flows is characterized by three functions: the shear-stress function and two normal stress functions. This remains true for simple semi-liquids, but now the limits of these functions as the rate of shear goes to zero need not be zero but may approach critical non-zero values. This fact allows the existence of plugs. This paper gives explicit procedures for determining the size of plugs for the entire variety of viscometric flows analyzed in the book mentioned above.