In this work we present investigation of the escape cones of null-geodesics from the interior of rotating homogeneous compact stars in the model, where only terms linear in the star’s rotational frequency are assumed. We focus on the single model of the star with particular radius R = 2.8M (using units in which c = G = 1) rotating with different values of angular momentum J. We vary the position of the isotropically radiating source both in radial and latitudinal direction and we show the impact of the position and the rotational rate on the shape of the escape cone of null-geodesics. We find that even for small rotational rate corresponding to j = J/M^2 = 0.1 the impact on the escape cones is rather strong. The escape cones are no longer symmetrical around radial direction, and it is clearly seen that the radiation in the direction of the rotation can easily reach the infinity. On the other hand, the radiation in the direction opposite to the rotation will be trapped in the interior of the star. We discuss possible astrophysical relevance of our results.