Carbon isotope labeling method is a standard metabolic engineering tool for flux quantification in living cells. To cope with the high dimensionality of isotope labeling systems, diverse algorithms have been developed to reduce the number of variables or operations in metabolic flux analysis (MFA), but lacks generalizability to nonstationary metabolic conditions. In this study, we present a stochastic simulation algorithm (SSA) derived from the chemical master equation of the isotope labeling system. This algorithm allows to compute the time evolution of isotopomer concentrations in non-stationary conditions, with the valuable property that computational time does not scale with the number of isotopomers. The efficiency and limitations of the algorithm is benchmarked for the forward and inverse problems of 13C-DMFA in the pentose phosphate pathways, and is compared with EMU-based methods for NMFA and MFA including the central carbon metabolism. Overall, SSA constitutes an alternative class to deterministic approaches for metabolic flux analysis that is well adapted to comprehensive dataset including parallel labeling experiments, and whose limitations associated to the sampling size can be overcome by using Monte Carlo sampling approaches.