Pt microdisk electrodes of diameter 10-70 ..mu..m sealed in glass, lying in the same plane with Ag pseudoreference and Pt auxiliary disk electrodes, and coated with a few micrometers of ionically conducting polymer film containing electroactive solutes provide a convenient experimental microcell format for solid-state linear sweep and cyclic voltammetry of the electroactive solutes. Transport rates of the solutes in the polymer depend on composition of the bathing (plasticizing) gas around the microcell, the temperature (polymer fluidity), and solute charge, size, and physical diffusion vs. electron self-exchange rates. Investigation of such transport phenomena requires theoretical analysis of the transport geometry of the microcell, which is the main subject of this paper. The preferred situations for measurements of transport rate are (i) polymer films thick in comparison to electrode diameter and transport rate, so that semi-infinite transport applies, and (ii) films thin in the same respects, so that currents are a summation of thin layer cell and microcylindrical geometries. Measured diffusion constants are confirmed with data from a four-electrode interdigitated array electrode experiment.