A theoretical ground motion model based on seismic source models has been applied to the available strong-motion acceleration recordings in Iceland. The source parameters have been estimated from the acceleration records and different estimation methods are studied. The applied model is used to study the characteristics of strong ground motion with the main objective of improving models for seismic hazard studies. The applied ground motion model is useful for describing the attenuation of ground motion parameters such as peak ground acceleration, root mean squared acceleration and spectral acceleration. The model can also be used for simulating realistic input records for computational structural models using a stochastic approach. A comparison of the results for the attenuation of the ground motion parameters obtained from the Icelandic data is compared with results from North-America and Europe by applying the theoretical model to other datasets as well as considering attenuation relations found in the literature. The models are applied to specific earthquakes as well as earthquakes with similar magnitude and similar source mechanism. Special consideration is given to near field acceleration as well as rate of attenuation.