The two-dimensional vehicle routing problem (2L-VRP) is a realistic extension of the classical vehicle routing problem where customers' demands are composed by sets of non-stackable items. Examples of such problems can be found in many real-life applications, e.g. furniture or industrial machinery transportation. Often, these real-life instances have to deal with uncertainty in many aspects of the problem, such as variable traveling times due to traffic conditions or customers availability. We present a hybrid simheuristic algorithm that combines biased-randomized routing and packing heuristics within a multi-start framework. Monte Carlo simulation is used to deal with uncertainty at different stages of the search process. With the goal of minimizing total expected cost, we use this methodology to solve a set of stochastic instances of the 2L-VRP with unrestricted oriented loading. Our results show that accounting for systems variability during the algorithm search yields more robust solutions with lower expected costs.