A viscosity equation is formulated on the basis of Oldroyd′s theory for elastic and viscous properties of emulsions and suspensions by considering the drops as cylindrical rather than spherical in shape. The problem is formulated in three dimensions using cylindrical coordinates. The result can be considered as applicable to liquid, circular disk particles with negligible thickness, such as platelets, in dilute suspensions. In the present analysis, initially, stress effects are assumed uniform along the length of the cylinder, the z coordinate of velocity decays exponentially with time, and the interactive effects of the particles are assumed negligible. The independent parameters are viscosity of the solvent and dispersant, η and η′, respectively, ratio of cylindrical radii a/b, a time derivative Δ = d/dt, and constant interfacial tension y. The present analysis is considered as the first step in analyzing the general problem of liquid cylinders suspended in liquids. Several different conclusions are reached compared with Oldroyd′s model.