Uncertainty quantification (UQ) is important for hyperbolic and kinetic equations due to possible modeling and measuring errors in equation of state, collision kernels, sources, initial and boundary data. The Stochastic Galerkin method is a popular and efficient method for UQ for partial differential equations but it encounters major difficulties for nonlinear hyperbolic systems of conservation laws since it gives a system which is not necessarily hyperbolic. We introduce a flux splitting for nonlinear hyperbolic systems that will avoid such a difficulty. For Boltzmann equation we introduce a fast and efficient spectral methods for its UQ.