This paper constructs two stochastic growth models of family capital with and without insurance mechanisms respectively, defines the probability of falling into the poverty trap, and computes it numerically by giving specific parameters of the random distribution. This paper analyzes whether insurance can help families get rid of the poverty trap caused by major emergencies with the methods proposed. The result of the research shows that after covering insurance, the probability of falling into the poverty trap is determined by two main effects: the effect of increasing capital and the effect of insurance compensation. Richer families can reduce the probability of falling into the poverty trap by covering insurance, and the higher the insurance proportion is, the smaller the probability will be. The probability of falling into the poverty trap of poorer families after covering insurance is ambiguous. Whether the probability will reduce depends on the sensitive coefficient of the critical capital for the premium rates. The probability of falling into the trap for both wealthier families and poorer families will decrease with the decline of additional premium coefficient.