The motion of a general class of gelling materials was investigated under a particular physical configuration. The gelling material was hypothesized to be a Bingham type body of constant viscosity and variable yield stress. The form of the time‐past deformation dependent yield stress has been proposed by Slibar and Paslay and incorporates an exponential memory function, which “weights” current deformation rates more heavily than those occurring at a previous time. The general constitutive equations used in this study were proposed earlier by Slibar and Paslay and in essence infer that no motion within the body is permissible for values of the square root of the quadratic invariant of the reduced stress tensor less than the yield stress. The physical configuration treated is that of a uniform layer of the proposed material extending over an infinite vertical plane. Hence, the stress field is a function of the material density and layer thickness only. The steady‐state solution was found for incipient flow and the necessary and sufficient criterion for solidification of the flow was determined. A numerical technique was used to obtain the time elapsed and total vertical displacement during the interim of relative motion, for various material parameters, felt by the authors to be in the practical range of interest. The results were found to meet all physically motivated anticipations; however, many different mechanisms are active in various gelling materials and the applicability of the proposed constitutive equations has to be verified in each case of a different material.