The paper proposes a model of demand for medical care under uncertainty. Both health capital and wealth are modelled as Wiener processes. The model uses a continuous time stochastic optimisation technique to derive optimal solutions for consumption, leisure and medical care. Insurance against uncertain medical expenditure is then incorporated into the optimisation problem under the assumption of constant relative risk aversion of the value function, and constant elasticity, relative risk aversion and relative prudence of the health investment function. The optimal solution is shown to depend on the curvature of the value function, the curvature of the health investment technology, and variances of the stochastic shocks. Dynamic simulations of the model are carried out.