This paper focuses on the problem of semi - infinite elastic body filled with the material which behaves differently in tension and compression . the contents include : ( 1 ) the solution of elasticity theory for the material incapable in tension is established by introducing heaviside function ; ( 2 ) the solution of elasticity theory with different modulus in tension and compression is established based on the solution of elasticity theory for the material incapable in tension and mindlin ' s solution ; ( 3 ) the solution of elasticity theory with different modulus in tension and compression is employed to analyze the stress of pile foundation ; ( 4 ) the solution of elasticity theory with different modulus in tension and compression is employed to analyze the settlement of pile foundation 本文考虑材料的拉压性能不同的特点，对半无限空间内部作用竖向集中力问题进行了新的研究，做了如下工作： ( 1 )引入heaviside函数，建立了不能承受拉应力材料的弹性理论解； ( 2 )基于不能承受拉应力材料的弹性理论解和mindlin解，建立了拉压模量不同材料的弹性理论解； ( 3 )将拉压模量不同材料的弹性理论解应用于桩基应力分析； ( 4 )将拉压模量不同材料的弹性理论解应用于桩基沉降分析。
