The travelling solvent floating zone (TSFZ) growth of Eu-substituted LSCO (La_1.81−xEu_xSr_0.19CuO₄, with nominal x = 0 ÷ 0.4) single crystals was systematically explored for the first time. The substitution of La with Eu considerably decreased the decomposition temperature. Optimal growth parameters were found to be: oxygen pressure 9.0–9.5 bars; Eu-free CuO-poor solvent (66 mol% CuO) with a molar ratio of La₂O₃:SrCO₃:CuO = 4:4.5:16.5 and growth rate 0.6 mm/hour. The obtained single crystals were characterized with optical polarized microscopy, X-ray diffraction and energy-dispersive X-ray spectroscopy analysis. The solubility of Eu in LSCO appeared to be limited to x~0.36–0.38 under the used conditions. The substitution of La³⁺ with smaller Eu³⁺ ions led to a structural transition from tetragonal with space group I4/mmm for La_1.81Sr_0.19CuO₄ (x = 0) to orthorhombic with space group Fmmm for La_1.81−xSr_0.19Eu_xCuO₄ (x = 0.2, 0.3, 0.4), and to a substantial shrinking of the c-axis from 13.2446 Å (x = 0.0) to 13.1257 Å (x = 0.4). Such structural changes were accompanied by a dramatic decrease in the superconducting critical temperature, Tc, from 29.5 K for x = 0 to 13.8 K for 0.2. For x ≥ 0.3, no superconductivity was detected down to 4 K.