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In Finte Element Methods (FEM), the solid model or the domain of interest is triangulated into small number of sub-domains called elements. This process, termed as mesh generation is a critical component of FEM in obtaining accurate solutions. Most of the time in the analysis is also spent in this component by an analyst. To alleviate this, viable alternative is the Meshless methods which have been gaining considerable interest in the ressearch community to certain class of problems in the solids and structers and fluid flow problems. As no mesh needs to be created, the node generation process, if fully automated, can result in substaintial savings in analysis time. Some questions still remain, namely, whether these methods are robust and viable for applications to general class of problems. Once such class of problem needs further attention is the applications of meshless methods to elastodynamics.