The present study is devoted to the analysis of basic turbulent premixed combustion closures applied to the numerical simulations of V-shaped flames. It is well known that an important parameter for the numerical simulation of such premixed turbulent flames is the description of the departure from the bimodal limit (thin flame limit), which is associated to the maximum value of the progress variable segregation rate, i.e., S = 1. The evolution of this segregation rate is often deduced from a modeled transport equation written for the progress variable variance. However, the closure of such a transport equation does involve many additional sub-models, which are related to the mean and variance progress variable fluxes and mean scalar dissipation rate of the progress variable variance. In the present work two original closures for the mean chemical rate are considered. Special emphasis is also placed on algebraic closures for S that circumvent the difficulty associated to the modeling of the second moment of the progress variable. In the first step of the analysis these closures are analyzed in the case of the propagation of a one-dimensional turbulent premixed flame brush. They are subsequently applied to the numerical simulation of premixed V-shaped flames that have been studied experimentally by Galizzi (2003) and by Degardin et al. (2006). It is found that these closures provide a satisfactory representation of the turbulent premixed flames.