Considering the vapour effects, we calculate the shape instability of single-bubble sonoluminescence (SBSL) in the phase diagram of the amplitude of driving pressure versus ambient radius, i.e. the pa - R0 diagram. The numerical calculation shows that the results calculated by the present model are reliable, even some parameters,such as the binary diffusion constant and the thermal conductivity of the mixture of argon and water vapour inside the bubble, are roughly evaluated. It is found by numerical calculation that the shape stable area of a single argon bubble in those viscous liquids with low vapour pressure, such as oil of vitriol, glycerol and 1,2-propanediol, can be extended to a wider region. Combining with the calculation of the maximum temperature inside the bubble, we may predict that these areas are probably the stable region of SBSL.