This paper develops techniques for equivalent circuit analysis of tight epithelia by alternating-current impedance measurements, and tests these techniques on rabbit urinary bladder. Our approach consists of measuring transepithelial impedance, also measuring the DC voltage-divider ratio with a microelectrode, and extracting values of circuit parameters by computer fit of the data to an equivalent circuit model. We show that the commonly used equivalent circuit models of epithelia give significant misfits to the impedance data, because these models (so-called "lumped models") improperly represent the distributed resistors associated with long and narrow spaces such as lateral intercellular spaces (LIS). We develop a new "distributed model" of an epithelium to take account of these structures and thereby obtain much better fits to the data. The extracted parameters include the resistance and capacitance of the apical and basolateral cell membranes, the series resistance, and the ratio of the cross-sectional area to the length of the LIS. The capacitance values yield estimates of real area of the apical and basolateral membranes. Thus, impedance analysis can yield morphological information (configuration of the LIS, and real membrane areas) about a living tissue, independently of electron microscopy. The effects of transport-modifying agents such as amiloride and nystatin can be related to their effects on particular circuit elements by extracting parameter values from impedance runs before and during application of the agent. Calculated parameter values have been validated by independent electrophysiological and morphological measurements.