The nucleation and lateral growth are more and more important steps for the thin film growth of a phase (silicide, intermetallic…) when the thin film thickness is in the range or below 10 nm. It might become crucial for contact in microelectronics that are in this range of thickness for actual devices and affect the properties of contacts in different parts of the devices. For reaction between 10 nm Ni(10%Pt) and (100)Si, it was shown that NiSi grows by nucleation and lateral growth at the epitaxial θ-Ni2Si/Si interface and forms precipitates having a large aspect ratio (large diameter and small thickness) were observed. In this work, the precipitate shape as well as the shape of the different interfaces close to the triple line are reproduced by using the model of Pasichnyy and Gusak for θ-Ni2Si/Si interfaces that are either curved or straight. The deduced interfacial energies and kinetics parameters enabling to obtain the characteristics of the precipitates are discussed and compared to the ones obtained by the model of El Kousseifi et al. The conditions for mechanical equilibrium and the implication for the contact formation are discussed.