In the analysis of slug flow under gravity conditions surface tension is usually neglected. The liquid slug is treated as a homogeneous mixture and the liquid film adjacent to the wall, in the Taylor bubble zone behind the slug, is treated using the one-dimensional approach (channel flow theory). Although the use of the one-dimensional approach is not accurate, especially close to the bubble cap, it is considered as a valid approximation and it yields reasonable results for the modeling of pressure drop, bubble length and void fraction in slug flow. Since for the case of microgravity flow, surface tension is expected to be a dominant force that should not be overlooked, one may be tempted to use the same procedure for the analysis of slug flow under microgravity conditions with the surface tension included (this can be done also for non-microgravity conditions). In this work, it is shown that the inclusion of the surface tension in the one-dimensional approach for the film analysis leads to erroneous and unacceptable results near the bubble cap that cannot be used even as an approximation. It is also shown that far away from the cap the solution with and without the surface tension is practically the same. Thus, a simplified model for slug flow in microgravity is suggested that assumes a spherical shape of the bubbles at the nose that is matched with the conventional one-dimensional viscous solution far downstream. In this procedure the effect of surface tension at the nose is in fact taken into account indirectly by the imposition of a spherical cap. That is, the assumption that the bubble nose behaves similar to the behavior of small size bubbles that are controlled by surface tension.