The need for petroleum refineries to process different types of crude oil in order to maximise profit margin and to meet demand for products, calls for flexibility in the design and optimisation of crude oil distillation systems comprising distillation units and the heat recovery network. Crude oil distillation is a complex, capital- and energy-intensive process. The large number of degrees of freedom (column structure and operating conditions) and complex interactions within the system make the design and optimisation of crude oil distillation system a highly challenging task. This work develops new methodologies for the design of crude oil distillation systems that process a single crude oil feedstock and multiple crude oil feedstocks. In this work, the crude oil distillation unit is modelled using a rigorous tray-by-tray model where the number of trays active in each section is also a design degree of freedom. The model is embedded in an optimisation framework, together with a heat recovery model (applying pinch analysis), for design of an energy-efficient and cost-effective distillation system. The optimisation framework addresses both structural and operational degrees of freedom of the system, capturing the trade-off between capital and energy costs, and accounting for heat integration. The distillation model is built in Aspen HYSYS, while the optimisation is carried out in MatLab using a genetic algorithm, where data is exchanged during process simulation and optimisation. To overcome the shortcomings of the rigorous distillation model in the context of system optimisation, surrogate models based on artificial neural networks (ANN) and a support vector machine (SVM) are developed and applied in the optimisation framework. The ANN model simulates the crude oil distillation unit, while the SVM partitions the search space, increasing the likelihood that the optimised solution will converge when simulated using a rigorous model. The SVM helps to reduce computational effort by focusing the search on potentially feasible solutions. Both the ANN and SVM are fitted to results of multiple rigorous simulations of the distillation unit. The proposed surrogate modelling approach is extended to take into account multiple crude oil feedstocks in the design of the distillation unit. The distillation column models for multiple crude oils and heat recovery model are embedded in a two-stage optimisation framework, in which a hybrid stochastic-deterministic approach is applied to optimise structural variables and distillation column operating conditions. The overall objective is to maximise net profit while meeting product quality (and flow rate) constraints. The capabilities of the proposed methodologies are illustrated using industrially-relevant case studies. Results indicate that the used of surrogate model instead of rigorous models reduces computational time without compromising solution accuracy and optimality. The design approach to account for flexible operation is shown to identify effectively design alternatives that are economically viable and operable over the range of crude oil feedstocks.