In this paper a computational model for magnetization losses in HTS magnets is presented. The model is based on a semianalytical expression derived for the hysteretic energy loss density per cycle in HTS tapes due to changing external magnetic field. The real magnetic field dependent electric field-current density characteristic of HTS material, the geometry of the tape cross-section and the orientation of magnetic field are taken into account. Using the model the dependence of hysteresis losses on the orientation and amplitude of external magnetic field are studied. Furthermore, the model is applied to five solenoidal HTS coils which are wound of tape conductors having different aspect ratios. Special attention is paid to the differences in energy loss distributions between coils. The results show that in the coils wound of tape having aspect ratio higher than 3 the loss maxima are mainly caused by the radial component of magnetic field. Averaged losses in the magnet are investigated as a function of ramping frequency and the peak value of the operation current of coils.