Flame spread over a melting thermally thick composite polymer is investigated in a channel flow above a condensed fuel. The condensed fuel consists of an isotropic (melted layer of) liquid near the heated surface and an anisotropic (not-yet-melted) solid surrounding it. The influence of the solid anisotropy is evaluated by changing the solid conductivity (ksx or ksy) in one particular direction (x in horizontal flame spread direction or y in vertical direction, see schematics in Figure 1) while keeping the other properties fixed. Note that the liquid conductivity kl has no isotropic behavior. Numerically, it is found that the flame spread rate decreases with either increasing ksx or ksy. The decrease with respect to ksy is less than for a comparable case described by the de Ris formula for an isotropic pure solid. The flame spread rate is more accurately determined by an analytical formula derived for spread across a melting solid fuel. Qualitatively, the liquid layer extent decreases with either increasing ksx or ksy due to the role played by the solid conduction as a heat loss mechanism in a thermally thick fuel. In addition, ksy more strongly influences the extent of the liquid layer than ksx in that it changes both the horizontal and vertical boundaries of the liquid layer. The surface parameters and energy balance show the dependence of the flame size on ksx and ksy. Generally, the size of the spreading flame decreases with either increasing ksx or ksy. The influence of the condensed phase anisotropy is also studied by the influence of other overall quantities such as the heat flux region, the mass flux region, and the ignition delay.