In a structural analysis, dynamic response of a crack is of significant importance as well as the impacts of elastic waves on stress intensity factors (SIF). In this paper, dynamic analyses of multiple cracks on a half-plane subjected to anti-plane shear stresses are presented. Stress intensity factors are calculated and the interaction of elastic waves with the boundary of plane and the cracks' tips is investigated at different locations. The distribution discontinuous displacement techniques are used, enabling us to solve the crack problems in dynamic fracture mechanics. Integral transformations (Laplace and Fourier) are applied to elastodynamics equations and by using a set of appropriate boundary conditions solved discontinuous displacement and the crack problem is solved through discontinuous displacement method. As a result, the stress equations with hypersingularity terms are obtained. Using Chebyshev series expansion and collocation points in Laplace domain, the crack solution is achieved. Finally, different algorithms of numerical Laplace inversion are presented and the stress intensity factors (SIF) are obtained. The presented results are compared with published data and a good agreement is observed. Moreover, it is also demonstrated that the present theoretical study is capable of modelling multiple cracks with different arrangements.