本文主要應用無元素法(Meshfree method)家族中一員，微分再生核近似法(Differential Reproducing Kernel Approximation, DRKM )來分析二維彈力的問題，藉以驗證此法之適用性與可行性。本法以微分再生核近似配合適點法(Point collocation method)來分析微分方程，以簡便的微分法則大大簡化了繁雜的求導數過程，最大的特點為完全使用離散點來建構數值模型，排除使用積分網格，真正作到無元素法的精神。在本文中，將使用DRKM來分析彈性樑承受外力時的變形、含圓孔無限平板應力集中以及裂縫之應力強度因子。分析時以離散再生核近似的法則求出再生核形狀函數(Reproducing Kernel shape function) 及其各階導數。再由各問題之控制方程式，建立分析問題所需聯立代數方程組求解。

數值算例顯示，求解懸臂樑問題時，幾乎可達到解析解的精度。在求解含圓孔之無限板，裂縫等有局部應力集中問題時，只需在局部節點加密即可達到良好的精度。

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