In present work, a novel bubble distribution model, based on the population balance of bubbles, is proposed incorporating with the Navier-Stokes equation for solid flow in order to predict the solid mixing and circulation as well as the bubble behavior in bubbling fluidized beds. This work is comprised of three sections: The first section is "estimation of solid flow pattern in bubbling fluidized bed". In this section. we compare the computed values of bubble diameter and solid velocities with experimental values in cylindrical bubbling fluidized bed. The second section is "estimation of solid flow pattern in rectangular fluidized beds". This section is divided into two parts. In the first part, we apply the simulation model to bubbling rectangular fluidized bed, which is expressed by the rectangular coordinate system in place of the cylindrical coordinate. In the second part, we compute the solid behavior in beds equipped with immersed vertical tubes. Third section is "solid mixing in bubbling fluidized beds". This section is also divided into two parts. In the first part, we investigate experimentally the solid mixing characteristic in bubbling fluidized beds using the tracer particle. In the second part, we incorporate the simulation model with a solid dispersion model for predicting the solid mixing in bubbling fluidized beds.