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Unsteady laminar flame propagation confined in a closed cylindrical combustion bomb is studied by numerical computation for an axisymmetric two-dimensional laminar flame. Computation includes complete two-dimensional unsteady Navier-Stokes equations of change for a chemically reacting propane-air mixture. Implicit Continuous fluid Eulerian, Arbitrary Lagrangian Eulerian finite difference technique, simplified reaction kinetics models, and artificial flame stretching transformation and inverse transformation were adopted in the calculation. Physically realistic flame behavior can be demonstrated even with rather coarse computing cell size, simplified reaction kinetics models, and personal computer level low power computing machines.