Recent work with nested horizontal grid networks in the solution of systems of geophysical equations is briefly reviewed. The horizontal nesting technique utilized in the experiments described in this paper is the three-dimensional analogue to that used by Harrison and Elsberry in one- and two-space dimensional tests. Several variations of the model, with both single, abrupt grid increment changes and more gradual reduction to the smaller scale are described. Three-dimensional experiments utilized an analytic initial state representing a tropical storm scale disturbance. Development was stimulated by means of imposed diabatic heating linked to the moving low center in the frictionless, multilevel primitive equation model. Development and movement of the simulated disturbance in single and multiple grid reduction models are compared to results obtained in a uniform coarse grid model. Initialization of the nested grid system is accomplished by means of a divergence or “balance” equation derived from the finite-difference form of the primitive equations. Results obtained suggest possible application of the meshing technique to operational numerical prediction models.