An important issue arising in supercritical steam boilers is to avoid the tube wall overheating due to high heat fluxes transferred from flue gases to the fluid. The paper presents a new hybrid one/two-dimensional model of the fluid heating in waterwall tubes in the combustion chambers of steam boilers for supercritical steam parameters. The model is based on distributed parameters. The analysis concerns tubes with externally finned surfaces. Using the proposed model, it is possible to estimate zones and locations where the tube wall overheating may occur. One-dimensional equations describing the mass, momentum and energy conservation are formulated and solved for the fluid domain. Each analyzed cross section of the finned waterwall tube is divided into 20 control volumes for which energy balance equations are solved in a two-dimensional space. In order to analyses the conjugate heat transfer between the waterwall tube and the fluid, the heat transfer coefficient is computed using the Kitoh correlation. The computations assume a variable heat flux along the combustion chamber height. Also, the heat flux variation on the waterwall tube circumference is incorporated within the model. The reduction in dimensionality in both the fluid and the solid domains leads to an improvement in the computational performance compared to complex three-dimensional computational fluid dynamics simulations. The paper presents an application of the proposed hybrid model to simulate heat and flow processes occurring in waterwall tubes of a supercritical boiler operating in one of the Polish power plants. The results of the simulations are compared with the data obtained from measurements and good agreement is obtained. Therefore, the developed model can be successfully applied, e.g. in simulators of the supercritical power boiler operation.