Neutron powder diffraction studies of the R3Cu4Sn4 (R=Tb, Dy, Ho, Er) intermetallic compounds with the orthorhombic Gd3Cu4Ge4-type crystal structure indicate the existence of different magnetic structures. Rare earth atoms occupy two nonequivalent 2d and 4e sublattices. For R=Tb and Dy the magnetic structures below the Néel temperatures equal to 17.5 and 15K, respectively, are described by the propagation vectors k=(0,0,1/2+δ). In these compounds both rare earth sublattices order and do not change up to the Néel temperatures. For R=Ho the magnetic structure is more complicated. There are two vectors; one of them is k=(0,1/2,0) whereas the second one changes with temperature. For the Er compound there is the propagation vector k=(1/2,1/2,0) which describes the magnetic ordering in the 2d sublattice and at low temperatures it is accompanied with the propagation vector k=(0,0,δ) describing the ordering in the 4e sublattice.