Different types of mechanical and thermal shock loads are considered to investigate transient stress intensity factors of two/three dimensional cracked specimens via meshless method with linear test function. Steady state and transient analyses show that the method is reliable. The effect of crack length, density and Lord-Shulman relaxation time on stress intensity factors are studied. Results represent the different effect of crack length on mechanical and thermal stress intensity factors. Various theoretical and real values of relaxation time are used to show how thermal stress intensity factor curves change when modified Fourier heat conduction law is employed compared with classical Fourier law. Additionally, the effect of specimen size on non-Fourier thermal stress intensity factor curves is investigated. We observed that using a functionally graded material instead of a composite coated substrate reduces local mean and peak values of transient thermal stress intensity factors.