A transport equation for the flame surface density is used to describe premixed turbulent combustion in the simple case of a one-dimensional propagation in a homogeneous mixture. An analytical method of the type devised by Kolmogorov, Petrovski and Piskunov, as well as numerical simulations, are exploited to study the influence of turbulence and laminar flame speed on the turbulent flame speed and on the turbulent flame thickness. It is shown that the model exhibits steadily propagating turbulent flames and that flame speed is proportional to the square root of the turbulent viscosity multiplied by the effective strain rate of the flow. If these two quantities are evaluated with classical expressions one finds that the turbulent flame speed is proportional to the square root of the turbulent kinetic energy (St= λAu′). This result agrees well with other experimental and theoretical expressions and correlations available in the literature. The comparison with experiments yields one of the constants of the model. The nonsteady formation of the turbulent flame brush is then examined to complete the description of the turbulent combustion wave dynamics. Two characteristic times of the turbulent ignition processes are revealed and the flame initiation is described analytically and numerically. The calculations indicate that the transport equation used to model the balance of flame surface provides a suitable description of turbulent flame propagation in one dimension. In addition, the results may be used to adjust the constants appearing in the balance equation for the flame surface density.