CD "Rannap. Time Knots", Klaveripoeg (2023). Rein Rannap (piano, prepared piano, harpsichord, celesta, harmonium, Rhodes electric piano, Hammond organ, digital and analog synthesizers, looper)
CD "The piano comes to visit you. The best of concert tours", Klaveripoeg (2022). Rein Rannap (piano), Mihkel Mattisen (piano)
CD "Rannap. Ever & Forever", Klaveripoeg (2020). Rein Rannap (piano), Jaanus Karlson (electronics)
3 CD-s "Rein Rannap. 58 parimat lugu" [58 best songs], Hitivabrik (2018). Artur Rinne, Joel de Luna, Mati Kõrts, Jassi Zahharov, Mait Trink, Taavi Peterson, Kristjan Kannukene, Rein Rannap, Mihkel Mattisen, Lenna, Ott Lepland, Uku Suviste, Silvi Vrait, Heidy Tamme, Ivo Linna, Meelis Hainsoo, Maarja, Kirile Loo, Tõnis Mägi, Marju Kuut, Jaak Joala, ensemble Pirita, Rein Rannap Ensemble, Ruja, Henn Rebane Ensemble, ensemble Keelatud!, ensemble 2Ühel, ensemble Fix, ensemble Hõim, ensemble Noor Eesti, The XXI Century Orchestra, Estonian Radio VAriety Orchestra, Estonian Philharmonic Chamber Choir, Choir Studio Ellerhein, Estonian National Male Choir, conductors Erki Pehk, Rostislav Merkulov, Paul Mägi
CD "Tagasirändur", Full House Agency (2018); Ott Lepland (vocal), Rein Rannap (piano, electric piano), Raun Juurikas (keyboards), Jörgen Pakkas (guitars), Viljar Norman (bass), Kristjan Mängel (percussion), Elis Loik, Kristiina Renser, Karl-Erik Tamme (backround vocals), Kristjan Jõemägi (percussion)
CD "Selfies with Classics", Klaveripoeg (2018); Rein Rannap (piano)
CD „Banned! Estonia's first rock album. 43 years later. Estonian rock group Ruja early songs 1971–1973“, Klaveripoeg (2016); Kristjan Kannukene (vocal), Pent Järve (guitars), Siim Usin (bass), Hans Kurvits (drums), Rein Rannap (piano, Hammond), Chamber Choir Collegium Musicale, conductor Endrik Üksvärav
CD "Idyll. Piano Solos", Klaveripoeg (2013); Rein Rannap (piano)
CD „2 in One; Rannap & Mattisen“, Klaveripoeg (2012); Rein Rannap and Mihkel Mattisen
CD „Hingelinnud“, Klaveripoeg (2011); Estonian Television Children's and Toddlers' Choir, soloists Bonzo & Kaisa Padur, Tallinn Chamber Orchestra, conductor Toomas Vavilov
CD "Ilus maa" [Beautiful Land], Klaveripoeg (2009); ensemble Kosmikud, Rein Rannap (piano and Hammond-organ), girls’ choir Ellerhein, Estonian National Male Choir (cond. Tiia-Ester Loitme), Laur Joamets (guitars), Vambola Krigul (percussion), Priit Volmer (bass-baritone)
CD "Klaveri kuld" [Piano Gold], Klaveripoeg (2009); Rein Rannap (piano)
CD "Klaver tuleb külla. 10, parimad palad" [Piano Comes for Visit 10, The Greatest Hits], Klaveripoeg (2007); Rein Rannap (piano)
CD "Läbi jäätund klaasi" [Through A Frozen Window], Klaveripoeg (2006); Maarja-Liis Ilus (vocals), Rein Rannap (piano), The XXI Century Orchestra, conductor Erki Pehk
CD "Tantsib klaveril" [Dances on the piano], Klaveripoeg (2004); Rein Rannap (piano)
4 CDs "Varajased laulud" [Early Songs], hyper.records (2002); H. Tamme, T. Mägi, M. Kuut, R. Linna, I. Linna, J. Joala, M. Aare, S. Vrait, M. Nuude, E. Himma, A. Veski, J. Steinfeldt, K. Tomingas, K. Loo, J. De Luna, Estonian Radio Dais Orchestra, R. Rannap’s group, ensembles Fix, Pirita, Kuldne Trio, Dr. Friedrich, Ruja, Hõim, Noor Eesti, T. Kadajas, U. Alender and others
CD "Maasikad : Reinuvaderi ja karuoti laulud" [Strawberries : Fox and Bear Songs], Hitivabrik (2003); Estonian Radio Song Children, instrumental ensemble: Rein Rannap (keyboards), Ain Varts (guitars), Raul Vaigla (bass guitar), Toomas Rull (percussion)
2 CDs "Need ei vaata tagasi... Osa 1" [These won't look back... Part 1], HyperElwood (1999); Ruja
3 CDs "Need ei vaata tagasi... Osa 2" [These won't look back... Part 2], HyperElwood (1999); Ruja