This paper presents a theoretical treatment of the critical heat flux on metal-graphite composite surfaces. A previous study found that the tips of graphite-fibers act as bubble nucleation sites. Throughout the transition boiling regime, vapor rises into liquid on the nodes of the Taylor waves in reference to the Rayleigh-Taylor instability theory. At the critical (i.e., maximum) heat flux, this rising vapor forms into jets. These jets come from the graphite fiber tips that are arranged in an equilateral triangular grid in the metal matrix. The basic spacing of the grid is the two-dimensional Taylor wavelength, which is the spacing of the most basic module of jets. At the peak heat flux, the Kelvin-Helmholtz instability causes the jets to become unstable and brings about burnout. In other words, this instability theory predicts when the vapor velocity in the jet will reach a critical value to cause the vapor jets to cave in. The existing empirical results indicate that the nucleate pool boiling curves for metal-graphite composites of different graphite concentrations (i.e., area fractions) congregate near the critical heat flux of the composite for the optimum performance as the degree of superheat increases. With this particular graphite-fiber concentration known, a balance of the heat flux by the latent heat carried away in the jets when the liquid is saturated yields the maximum (i.e., critical) heat flux equation. Both copper-graphite and aluminum graphite composites are treated.