Soil is a complex material whose properties are elastic, plastic and viscious. The selection of a proper constitutive relation is important in the study of stratum movement induced by underground excavation in modern cities. First, based on the Fast Lagrangian Analysis of Continua (FLAC) method, the elastic response stress (p, q) distribution induced by a circular tunnel is analyzed, and the surrounding soil is divided into four categories: p increase q increase, p increase q decrease, p decrease q increase, p decrease q decrease according to p-q stress path. The character of p-q distribution and the plastic zone induced by tunneling in clay are compared when the Mohr-Coulomb model (M-C), the Drucker-Prager model (D-P) and the Modified Cam-Clay model (C-C) are adopted; the C-C model is considered to be suitable for simulating underground excavation problems. Second, factors such as stratum character, stress path and relative position between soil and excavation are thought to be important in the selection of a proper constitutive relation, accounting for the geological condition of Beijing and measuring techniques being used in geotechnical engineering. Fine grained soils such as clay and silt can be modeled by the C-C model. Coarse grained soil, for containing and not containing excavation, may be represented using the M-C model considering strain softening and the normal M-C model. Finally, with the aid of FLAC method and its internal language FISH, a scheme of estimating and controlling parameter input is suggested.