CCD surface photometry of 47 radio galaxies in the R-band is reported. The goal of the programme is to study the relationship of the properties of the parent galaxies to the radio structure and, in particular, to look for differences between Fanaroff & Riley (FR) class I and II sources. In order to clarify some ambiguous cases in the FR classification, we define Classical Double, Twin Jet and Fat Double sources. We describe our definitions of these three classes and their relation to the FR classification. We then show that Classical Double sources are generally associated with normal giant elliptical galaxies with absolute magnitudes near |$M^\ast$| of the Schechter luminosity function and are mostly considerably fainter than first-rank galaxies in rich clusters. Twin Jet and Fat Double sources, on the other hand, are associated with brighter galaxies. These galaxies are also larger and have flatter optical brightness distributions than most giant ellipticals. They can generally be described, following Mathews, Morgan & Schmidt, as D or cD galaxies. These results imply that Classical Doubles (FR II) with |$P_{1400}\lesssim 3\times 10^{26}\enspace\text {W} \enspace \text {Hz}^{-1}$| cannot normally evolve into Twin Jet (FR I) sources, since the two classes are associated with different types of galaxies. We suggest that Classical Doubles are essentially transient, whereas Twin Jet sources are more stable, with longer lifetimes.