The optical properties of tubular aggregates formed by self-assembly of zwitterionic meso-tetra(4-sulfonatophenyl)porphyrin (TPPS4) molecules are studied through a combination of experimental and theoretical techniques. The interest in these systems, with diameters of 18 nm and lengths extending up to micrometers, derives from their strong interaction with light and their similarity to natural light-harvesting systems for photosynthesis. The absorption and linear dichroism spectra are obtained in the spectral region from 300 to 750 nm, which includes the exciton bands deriving from the molecular B (Soret) as well as the Q transitions. We demonstrate that a Frenkel exciton model which takes into account the four dominant molecular excited states (Bx, By, Qx, and Qy) provides a good global fit to the experimental spectra. From comparison between theory and experiment, we propose a detailed molecular structure within the nanotube.