A theoretical study of population II variables with periods in the range 10 - 20 days (W Virginis variables) is presented. A modified hydrodynamic Christy code is used in conjunction with the Carson opacities, in preference to the Los Alamos tables, following the work of Carson, Stothers and Vemury on the shorter period BL Herculis variables. Twenty-five survey models are presented, along with nine other comparison models of varying masses and opacities. A study of the observations shows that the division of these variables into two types by observers might be explained by a slightly different mass for each type, thus making the division dependent on the star's previous evolution. The non-linear results obtained by this study show that a mass of 0.6 M☉ is a good one to use, and that M = 0.5 M☉ makes little difference (although M = 0.8 M☉ seems to be too high). The results in general compare well with the observations, as both also show the split into two types of light curve. Three good models of individual stars are presented, on a par with the models of BL Herculis published by Carson, Stothers and Vemury. The bumps in the light and velocity curves of many of the models seem to be real, caused by the Christy "echo". A few of the models show some RV Tauri behaviour. One in particular shows very strange behaviour, involving a violent 81ternation of light curve shapes. Models constructed using the Los Alamos opacities do not produce results as consistent with observations as those of the main survey. The study shows that these stars can be represented by hydrodynamic models of mass 0.6 M☉ using the Carson opacities, but also that convection may be important in the cooler stars in order to model them accurately. This indicates the direction in which further theoretical work may lie.