The uniaxial strain (and pressure) derivatives of the critical temperature of superconductivity (Tc) of La2−xSrxCuO4 (LSCO) cuprate is studied within the extended Holstein–Hubbard model and bipolaronic mechanism of high-Tc superconductivity. The Tc of LSCO cuprate is associated with the Bose–Einstein condensation temperature, TBEC, of an ideal gas of the intersite bipolarons. Working on a modified chain model lattice of cuprates we expressed TBEC as a function of LSCO’s parameters (apical oxygen ion’s mass and its vibration frequency, the periods and the strains of the lattice). Using the experimental values of LSCO parameters the uniaxial strain derivatives and the uniaxial pressure derivatives of Tc i.e. ∂TBEC/∂ɛi and ∂TBEC/∂pi (i=a,c) of LSCO cuprate are calculated as a function of doping level x. The obtained results are compared with the available experimental data. Qualitative and quantitative similarities as well as differences in the doping dependencies of between our ∂TBEC/∂ɛi (∂TBEC/∂pi) and the experimental ∂Tc/∂ɛi (∂Tc/∂pi) (i=a,c) are discussed. Upon carried analysis we concluded that the uniaxial strain (pressure) derivatives of Tc of LSCO cuprate can be interpreted within the bipolaronic mechanism of superconductivity.