Protein phosphorylation is a very common post-translational modification, catalyzed by kinases, for signaling and regulation. Phosphotyrosines frequently target SH2 domains. The spleen tyrosine kinase (Syk) is critical for tyrosine phosphorylation of multiple proteins and for regulation of important pathways. Phosphorylation of both Y342 and Y346 in Syk linker B is required for optimal signaling. The SH2 domains of Vav1 and PLC-γ both bind this doubly phosphorylated motif. Here we used a recently developed method to calculate the effects of Y342 and Y346 phosphorylation on the rate constants of a peptide from Syk linker B binding to the SH2 domains of Vav1 and PLC-γ. The predicted effects agree well with experimental observations. Moreover, we found that the same doubly phosphorylated peptide binds the two SH2 domains via distinct mechanism, with apparent rigid docking for Vav1 SH2 and dock-and-coalesce for PLC-γ SH2.