This paper focuses on chance constraints containing linear matrix inequalities which are important in stochastic programming problems. We aimed to find efficient methods for transforming chance constraints to more familiar forms. Several methods are introduce that are based on probability inequalities, including Chebyshev inequality, Petrov exponential inequalities, etc. Making several assumptions, it is very efficient to use these inequalities directly for problems with chance constraints containing one-dimensional linear matrix inequalities. For multidimensional constraints, we introduced alternate approaches, since the probability inequalities derived for one-dimensional problems cannot be used directly. We found that we can transform chance constraints into familiar conic quadratic or quadratic constraints. Finally, we considered an example to test these methods and found that they work well.