The main goal of this study is to improve the modelling of the source mechanism associated with the generation of long period (LP) signals in volcanic areas. Our intent is to evaluate the effects that detailed structural features of the volcanic models play in the generation of LP signal and the consequent retrieval of LP source characteristics. In particular, effects associated with the presence of topography and crustal heterogeneities are here studied in detail. We focus our study on a LP event observed at Kilauea volcano, Hawaii, in 2001 May. A detailed analysis of this event and its source modelling is accompanied by a set of synthetic tests, which aim to evaluate the effects of topography and the presence of low velocity shallow layers in the source region. The forward problem of Green's function generation is solved numerically following a pseudo-spectral approach, assuming different 3-D models. The inversion is done in the frequency domain and the resulting source mechanism is represented by the sum of two time-dependent terms: a full moment tensor and a single force. Synthetic tests show how characteristic velocity structures, associated with shallow sources, may be partially responsible for the generation of the observed long-lasting ringing waveforms. When applying the inversion technique to Kilauea LP data set, inversions carried out for different crustal models led to very similar source geometries, indicating a subhorizontal cracks. On the other hand, the source time function and its duration are significantly different for different models. These results support the indication of a strong influence of crustal layering on the generation of the LP signal, while the assumption of homogeneous velocity model may bring to misleading results.