Key message Insurance might be an efficient tool to strengthen adaptation of forest management to climate change. A theoretical model under uncertainty is proposed to highlight the effect, on adaptation decisions, of considering adaptation efforts in forest insurance contracts. Results show that insurance is relevant to increase adaptation efforts under some realistic conditions on forest owner's uncertainty and risk preferences, and on the observability or not of adaptation efforts. Context One of the challenges of forest adaptation to climate change is to encourage private forest owners to implement adaptation strategies. Aims We suggest the analysis of forest insurance contracts against natural hazards as a vector to promote the implementation of adaptation efforts by private forest owners. Methods We propose a theoretical model of insurance economics under risk and under uncertainty. Results Our results indicate that when climate change makes the probability of the occurrence of the natural event uncertain, then it may be relevant to include adaptation efforts in the insurance contract, leading to an increase in the adaptation efforts of risk- averse and uncertainty-averse forest owners. In addition, we show that the relevance of insurance as a vector to promote adaptation efforts is greater when the forest owner's effort is unobservable by the insurer as compared to a situation of perfectly observable effort. Conclusion Under some realistic assumptions, the forest insurance contract seems to be a relevant tool to encourage forest owners to adapt to climate change.