Borehole instabilities can be encountered at any stage in the life of a well and they are the main cause of drilling difficulties, resulting in substantial expenditures, expensive loss of time, sometimes even in the loss of part of or even whole boreholes. The main aim of this research is to use new method and theory in geomechanics to conduct the stability analysis of wellbore. The cavity contraction theory is used to get the new elastic-perfectly plastic solutions for vertical borehole with anisotropic stress field. The solutions for Mohr-Coulomb and Hoek-Brown criteria are derived in this paper. A new alternative criterion, which is to limit the radius of plastic zone around borehole, to predict the wellbore instability was also recommended. The finite element code ABAQUS is applied to analyse the mechanical behaviour of wells with different inclinations and different azimuths. A Generalized Plane Strain Model is used in the calculation. The failure wellbore pressure, borehole closure, plastic zone distribution of different direction wells are given in this paper. In order to accurately predict the wellbore behaviour in soft and porous rocks, a suitable and advanced constitutive model of rocks is the key issue of the borehole instability research. A new model, called CASM (Clay And Sand Model) which is based on critical state theory and formulated in terms of the state parameter concept is applied in this research. The non-coaxiality theory is incorporated into CASM to analyse the wellbore stability. Compared with coaxial model, non-coaxial model gives more pessimistic results. However, it was found that the influence of non-coaxiality on wellbore stability depended on initial conditions of wellbore.