t A theoretical novel model of generalized photo-thermoelasticity and hyperbolic twotemperature theory is studied in this paper. The elastic medium is excited by an external magnetic field and pulsed laser based. The model is established in the context of memory-depended derivative (MDD) when the material is time-dependent. The governing equations describe the interaction processes for isotropic homogeneous hyperbolic thermoelastic medium in one-dimensional (1D) space when the non-Gaussian laser pulse model is applied with time delay. Moreover, The Laplace transforms is used to obtain analytical solutions of the main fields. As such, the medium is loaded when traction is free and shocked thermally with time-dependent. The complete solutions are obtained in Laplace time domain when the invers of Laplace transform are used numerically. Numerical results of the main quantities are discussed graphically with the effect of hyperbolic two-temperature when time-delay parameter is taken into account