A study on orientation of hyperspectral band cubes acquired with frame camera is presented in this paper. The camera technology is based on a tuneable Fabry-Perot Interferometer (FPI) and captures cubes of images sequentially using two sensors. However, the bands are not recorded at the same instant, which results different exterior orientation parameters (EOPs) for each image band. A technique based on polynomial model is assessed, which determines the EOPs within the hypercube from few sample bands, since a large number of bands are generated. Experiments were performed to assess the feasibility of using the polynomial technique. An analysis of the UAV trajectory was performed and the results of the polynomial technique were compared with those obtained by a conventional bundle adjustment. The trials showed that the results of both techniques were comparable, indicating that the time-dependent polynomial model can be used to estimate the EOPs of all spectral bands, without requiring a bundle adjustment including all bands. The accuracy of the block adjustment was analysed based on the discrepancies obtained from independent checkpoints. The root mean square error (RMSE) was calculated and showed an accuracy of approximately 1 GSD in planimetry and 1.5 GSD in altimetry. This accurate result is important because the proposed technique can significantly reduce the processing workload.