We study the optimal reinsurance policy and dividends distribution of an insurance company under excess of loss reinsurance. The insurer gives part of its premium stream to another company in exchange of an obligation to support the difference between the amount of the claim and some retention level. The objective of the insurer is to maximise the expected discounted dividends. We suppose that in the absence of dividend distribution, the reserve process of the insurance company follows a compound Poisson process. We first prove existence and uniqueness results for this optimisation problem by using singular stochastic control methods and the theory of viscosity solutions. We then compute the optimal strategy of reinsurance, the optimal strategy of dividends pay-out and the value function by solving the associated integro-differential Hamilton-Jacobi-Bellman Variational Inequality numerically in the case of a Poisson process with constant intensity.