The stability of a plasma toroidal configuration is affected by the component of the magnetic field curvature that lies within the magnetic surface. The analysis is simplified by introducing an appropriate one-dimensional model. Because the mentioned magnetic curvature component is periodic along the field lines and has a zero average, when the periodicity is shorter than a given amount no instability localized in a particular region along the field can be found. Then the stability analysis is reduced to consider modes that extend along the magnetic field and adapt themselves to the periodicity. Attention is also devoted to modes which arise when there is shear and the periodicity is relatively long.