The layered orthorhombic quaternary tellurides EuRECuTe3 (RE = Ho, Tm, Sc) with Cmcm symmetry were first synthesized. Single crystals of the compounds up to 500 μm in size were obtained by the halide-flux method at 1120 K from elements taken in a ratio of Eu/RE/Cu/Te = 1:1:1:3. In the series of compounds, the changes in lattice parameters were in the ranges a = 4.3129(3)–4.2341(3) Å, b = 14.3150(9)–14.1562(9) Å, c = 11.2312(7)–10.8698(7) Å, V = 693.40(8)–651.52(7) Å3. In the structures, the cations Eu2+, RE3+ (RE = Ho, Tm, Sc), and Cu+ occupied independent crystallographic positions. The structures were built with distorted copper tetrahedra forming infinite chains [CuTe4]7− and octahedra [RETe6]9− forming two-dimensional layers along the a-axis. These coordination polyhedra formed parallel two-dimensional layers CuRETe32−∞2. Between the layers, along the a-axis, chains of europium trigonal prisms [EuTe6]10− were located. Regularities in the variation of structural parameters and the degree of distortion of coordination polyhedra depending on the ionic radius of the rare-earth metal in the compounds EuRECuCh3 (RE = Ho, Er, Tm, Lu, Sc; Ch = S, Se, Te) were established. It is shown that with a decrease in the ionic radius ri(RE3+) in the compounds EuRECuTe3, the unit-cell volume, bond length d(RE–Te), distortion degree [CuTe4]7−, and crystallographic compression of layers [RECuTe3]2− decreased. The distortion degree of tetrahedral polyhedra [CuCh4]7−, as well as the structural parameters in europium rare-earth copper tellurides EuRECuTe3, were higher than in isostructural quaternary chalcogenides. Ab initio calculations of the crystalline structure, phonon spectrum, and elastic properties of compounds EuRECuTe3 (RE = Ho, Tm, and Sc) ere conducted. The types and wave numbers of fundamental modes were determined, and the involvement of ions in IR and Raman modes was assessed. The calculated data of the crystal structure correlated well with the experimental results.