The surface impedance and dispersion equation of a printed-circuit tensor impedance surface (PCTIS) are derived using a modified transverse resonance technique. A PCTIS consists of a subwavelength-patterned metallic cladding over a grounded dielectric substrate. The metallic cladding is analytically modeled as a tensor impedance sheet. An explicit expression is derived for the effective surface impedance of the PCTIS using a transmission-line approach. First, the surface-impedance expression is found for a printed-circuit scalar impedance surface using the transverse resonance technique. Next, a modified transverse resonance technique is applied to an idealized tensor impedance boundary condition (TIBC) to find its dispersion equation. Finally, the analysis of the printed-circuit scalar impedance is combined with that of the idealized TIBC to find the tensor surface impedance and dispersion equation of a PCTIS. A discussion of the principal axes and the propagation of TM and TE waves is provided. The special case of electrically thin PCTISs is also analyzed and discussed.