A new method of computing capsizing probability is described, This met
hod is based on a partially linear approximation of nonlinear terms in
the rolling differential equation. This substitution permits the rete
ntion of the topology of the nonlinear phase portrait and, at the same
time, the simplicity of the linear solution. A criterion of stability
of a system with partially linear righting moments is suggested. Fina
lly, a practical method of computer-aided calculation of capsizing pro
bability is described.