In the current paper, the peristaltic transport of a non-Newtonian fluid obeying a Casson model with heat and mass transfer inside a vertical circular cylinder is studied. The considered system is affected by a strong horizontal uniform magnetic field together with the heat radiation and the Hall current. The problem is modulated mathematically by a system of PDE that describe the basic behavior of the fluid motion. The boundary value problem is analytically solved with the appropriate boundary conditions in accordance with the special case, in the absence of the Eckert number. The solutions are obtained in terms of the modified Bessel function of the first kind. Again, in the general case, the system is solved by means of the homotopy perturbation and then numerically through the Runge-Kutta Merson with a shooting technique. A comparison is done between these two methods. Therefore, the velocity, temperature and concentration distributions are obtained. A set of diagrams are plotted to illustrate the influence of the various physical parameters in the forgoing distributions. Finally, the trapping phenomenon is also discussed.