Abstract Mathematical models of circulating fluidized bed (CFB) combustion systems vary from simple lumped models to full-scale 3D models with multi-phase flow fields. Models help to predict the behavior of the boiler under new operating conditions and to understand the underlying phenomena. Is it more important to make experiments or models? The answer is both. The real values can be assessed with the help of experiments and refined models. Is a complex model always better than a simple one? A simple model can be more easily modified and better adapted to the actual use. A 1,5-dimensional model of a CFB furnace is the simplest possible model that takes into account the most important heat transfer and flow features. Of these solids circulation is the most important factor that determines the amount of heat transfer at the furnace walls. Consequently, regulating the solids circulation is the fundamental means of load control in CFB furnaces. One dimensional model takes into account only the vertical flow direction, but 1,5-dimensional model considers solids circulation inside the furnace as well. The internal circulation is up to 2 times greater than the circulation around the solids separator and return in CFB combustors. 1,5-dimensional model is also called the core-annulus model. The furnace is considered as a cylinder with an annular space around it. The hot solids flow upwards along the cylinder and downwards along the annular space. In this study, a core-annulus model is implemented using a commercial IPSEpro software. The developed model consists of several modules. The mathematical principles of each module is described. The software is also presented briefly. The new model is applied to study the behavior of a large biomass boiler. The model inputs include mass flows of fuel and air, fuel type and parameters regarding the solids amount, size and distribution. In addition to inputs for the design operation, other scenarios are considered such as partial load and burning of different fuels. Strengths and weaknesses of the model are also assessed and pathways of future research are reviewed.