Uncertain weather conditions is one of the biggest challenges faced by air traffic route management. The US airspace is constructed of virtual freeways and all flights have predetermined routes on which to fly, which have originated over years of work and experience. These flight routes are sometimes marred by bad weather conditions which force the pilots to take on alternative routes. It is not very difficult to come up which these alternates if the conditions are known in advance but the real challenge comes when they come up unexpectedly enroute.Stochastic weather conditions such as turbulance and icing are very difficult to predict. For example the most reliable way to know that turbulance exists in a particular region is throug Pilot Reports. The National Center for Atmospheric Research (NCAR) uses mathematical models to get a rough estimate of these weather conditions. These conditions can be quite severe at times and can badly affect flight conditions resulting in unhappy customers.In this thesis I propose various problems, solutions and future directions of research dealing with stochastic weather conditions. As these conditions are not known with certainty, routes have to be planned which have a high probability of success and are robust to small variations.