As I write I am listening to Sergei Rachaminov's Vespers, Opus 37, for chorus and soloists. To my ears it is among the most characteristically Russian-sounding of any of Rachmaninov's music with which I am familiar. The fact that it is sacred choral music sung in Russian probably has a good deal to do with it. When I was a teenager I bought an LP of Russian liturgical music -- some composed in the 19th century, some traditional with older roots sung by a Russian choir in Germany, and I just fell in love with it. A proper Russian choir has at least a few impossibly deep-voiced bases able to sing notes lower than I can think of reaching, and they give the ensemble a sense of deep rootedness, as if the music is rising up from the good Russian earth and engulfing you.
The tradition in the Russian Orthodox church is not to have instruments, and perhaps partly as a consequence the harmonies are rather simple -- elemental? -- mostly open fifths and fourths. Rachmaninov's Vespers has much the same feel as the traditional Russian liturgical music, which was what I think he was going for. Op. 37 would be early in his career. His later music, undoubtedly influenced by western European music but unmistakably his, sounds (to me) more "romantic" than as distinctively Russian as this piece.
The Temecula Vintage Singers performed the Vespers the year before I joined (David Harmon, one of those impossibly deep basses, who later became a good friend, helped fill out the sound) so I have never sung this music. I am sure I would enjoy it, however.