Ignition with the help of a shock wave is performed by the interaction of accelerated plasma block by a petawatt-picosecond (PW-ps) laser, with a solid-state density fuel that it is a new possibility for achieving controlled fusion by inertial confinement. The unexpected production of plasma blocks provides new access to the ignition of solid-state density fuel according to the Chu hydrodynamic model. When the produced plasma block by the PW-ps laser hits the main fuel due to the density differences between the plasma block and the main fuel of the shock wave, this progressive wave increases the density of solidified fuels and reduces the energy of the ignition threshold and increases the flammability. In this study, a new discovery of shock waves has been observed leading to the resonance phenomenon. Nuclear heat shock waves resonance in the side-on ignition of fuel in the internal layer of fuel at x ≠ 0 appears from the exact solution of the hydrodynamic equations with respect to the density profile. This important finding achieves the required ignition temperature for solid-state fuel deuterium–tritium (D–T) in certain energies, with a significant increase due to the resonance of thermonuclear waves. This discovery will facilitate practical experiments on the ignition of advanced solid-state fuels with the accelerated plasma blocks by a PW-ps laser at certain energies.