Understanding the phenomenon of fracture is very important for many industrial applications. Numerical tools are needed to describe the crack pattern and the energies evolution in any specimen. Then, for example, the acoustic properties of any structure can be used for nondestructive testing. The aim of this article is to demonstrate the capabilities of the phase-field model for these processes. It can be used not only to study the wave propagation in materials consisting of several different materials or phases in composite pieces, but also to study the crack nucleation and propagation in homogeneous or composite materials. Numerical analysis of brittle fracture using the phase-field model is elaborated in this paper. We focus on the behavior of the linearly elastic bodies submitted under quasi static and dynamic loading. The influence of considering the kinetic energy on the dynamic phase-field pattern and on energies evolution is detailed. In fact, using the finite element method with Newmark scheme, we show the influence of the transverse wave and the celerity CT on energies evolution. Also, some numerical computations in quasi static fracture using phase-field model and staggered scheme will be elaborated. A qualitative agreement with experiments is shown. A comparison between quasi static and dynamic crack propagation is made.