Uncertainties inherent to convective weather represent a major challenge for the Air Traffic Management system, compromising operational safety and increasing costs. In this work, we address the multi-aircraft trajectory planning problem around stochastic storm cells. We implement an Augmented Random Search methodology to deform a nominal set of trajectories and look for a feasible solution. Its main objective is to guarantee minimum separation between vehicles and reduce time in risky regions. Through parallel programming on graphical processing units (GPUs), we reduce computational times to enable near-real time operation. We test the algorithm with two aircraft flying at the same airspeed and flight level; the scenario consists of real weather data given by an ensemble forecast. The influence of the maximum number of iterations is analyzed. Results reveal that our algorithm is able to avoid thunderstorms, solve conflicts between aircraft and reduce flight time in a few seconds. Key Words : Thunderstorm Avoidance, Multi-Aircraft, Conflict Solving, Parallel Programming.