This paper presents the theoretical analysis for the flow driven by surface tension and gravity force in an inclined circular tube. The previously developing equation for Power-Law model is a simple ordinary differential type. A governing equation is developed for describing the displacement of a non-Newtonian fluid(Casson model) that continuously flows into a circular tube by surface tension, which represents a second-order, nonlinear, non-homogeneous, and ordinary differential form. It was found that the theoretical predictions of the governing equation were in good agreement with the results for considering the Newtonian model.