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Experimental studies of the lattice parameters, thermal expansion, and elastic characteristics in the range of the structural phase transition in the YBaCo4-yZnyO7+x series of cobaltites with diamagnetic dilution of the cobalt subsystem have been carried out. It has been found that for stoichiometric samples annealed in vacuum, the parameter Delta a/a shows no features during the structural transition, while the parameters Delta b/b and Delta c/c experience similar jumps of different signs. This leads to a jump in anisotropic (rhombic) εo~-4·10-3 and isotropic (volume change) Delta V/V~ -1·10-3 deformations. Upon substitution with Zn ions, the orthorhombic distortion of the structure changes slightly, and the jump in the volume anomaly (linear thermal expansion) changes sign. Structure distortion in stoichiometric samples is accompanied by characteristic anomalies in the Young's modulus Delta E(T)/E0 and internal friction in the TS range, while for nonstoichiometric quenched samples, the anomalies completely disappear. The diamagnetic substitution with Zn ions leads to a sharp decrease and then complete disappearance of the jump in the curve Delta E(T)/E0. This may be due to a change in the ratio of isotropic and anisotropic deformation during the structural transition upon a small substitution in the cobalt subsystem. Keywords: frustrated systems, cobaltites, structural phase transitions, lattice parameters, isotropic deformation, anisotropic deformation, thermal expansion, Young's modulus, internal friction.

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