Development of a parallel unstructured multigrid solver for laminar flame simulations with detailed chemistry and transport. We develop a computer code for steady laminar flame simulations at low Mach numbers, with detailed models for chemical and molecular transport properties. The so called UG-C code is based on the UG library developed at IWR, Heidelberg. With a view to reducing computational time as much as possible, we combine an appropriate low Mach number modelisation with implicit time integration, Krylov-Newton and multigrid preconditioning, on unstructured dynamically refined grids, with storage optimization of sparse matrices. The code runs on distributed memory parallel machines, with several load balancing algorithms. We show applications to diffusion hydrogen/air and premixed methane/air flames. Multigrid acceleration has been obtained for sufficiently fine grids.