The joint inversion of Rayleigh wave group velocity dispersion and receiver functions has been used to study the crust and upper mantle structure at eight seismic stations in Cuba. Re- ceiver functions have been computed from teleseismic recordings of earthquakes at epicentral (angular) distances in the range from 30◦ to 90◦ and Rayleigh wave group velocity dispersion relations have been taken from earlier surface wave tomographic studies in the Caribbean area. The thickest crust (∼30 km) below Cuban stations is found at Cascorro (CCC) and Mais ́ı (MAS) whereas the thinnest crust (∼18 km) is found at stations R ́ıo Carpintero (RCC) and Guanta ́namo Bay (GTBY), in the southeastern part of Cuba; this result is in agreement with the southward gradual thinning of the crust revealed by previous studies. In the crystalline crust, the S-wave velocity varies between ∼2.8 and ∼3.9 km s–1 and, at the crust–mantle transition zone, the shear wave velocity varies from ∼4.0 and ∼4.3 km s–1. The lithospheric thickness varies from ∼65 km, in the youngest lithosphere, to ∼150 km in the northeastern part of the Cuban island, below Mais ́ı (MAS) and Moa (MOA) stations. Evidence of a subducted slab possibly belonging to the Caribbean plate is present below the stations Las Mercedes (LMG), RCC and GTBY whereas earlier subducted slabs could explain the results obtained below the Soroa (SOR), Manicaragua (MGV) and Cascorro (CCC) station