Abstract: The present paper deals with the shear flow of Johnson-Segalman fluid. On the basis of the analysis of the steady state solutions, it is obtained that a steady-state solution of JS model corresponds to a point on the steady total stress curve at which the total stress is T(X). When T is sufficiently small or sufficiently large , there is a single steady state solution , while there are three steady state solutions when T is intermediate in value. The steady state solution is judged to be stable or unstable in phase plane in this paper. At last , a new numerical scheme is devised by using backward finite difference method to solve JS model.

Key words: Johnson-Segalman fluid, shear flow, stability, difference method, non-newtonian fluid