Borehole volumetric strain and area strain observation models are the theoretical basis of the analysis of crustal rocks in strain measurement data and can help to reveal the physical nature of the research objects． Because parameter k ( the ratio between the area strain of inner walls of the strain instrument probe steel tube and that of empty hole rock ) is involved，the correct interpretation of model in the solution of k value becomes important． Since the applied stress needs to pass in the three layer medium of rocks，expansive cement and instrument steel cylinder，the calculation formula of k in the axisymmetric stress is deduced on the basis of thick wall cylinder equations in elasticity． The results of the formula is completely consistent with double bushing theory ( Pan Lizhou，Ouyang Zuxi and Chen Yuanjun ) ． The reliability of the formula is thus mutually proved． The paper also studies the affecting factors of k and provides the change curve and quantitative indexes． Finally，a comparison is made between this model and Evertson's two layers medium model ( rock，steel tube) with its k value of 0. 9 (1977) ． Points out the obvious differences between the two and the narrow scope of application 0. 9． The paper points out the differences between these two models and the limited applications of k value of 0. 9．