INTRODUCTION: Around 50 million people worldwide are affected by epilepsy. Despite efficiency and steady development of pharmacological treatments, every third patient suffers from intractable seizures. A surgical intervention may be the only solution in these cases. To identify the region for resection, neurosurgeons implant intracranial and subdural electrodes which are used to localize the epileptogenic zone from the measured potentials. AIM(S): Providing better tools for reliable reconstruction of sources of brain activity may lead to more precise localization of the seizure’s origin and better surgical outcomes. To reconstruct sources of brain activity, we use kernel approximation methods for the inverse problem (the reconstruction itself). We model the electric field generated by the neural activity (the forward problem) with finite element method (FEM). We use FEM as it enables the inclusion of realistic head anatomy and tissue properties in the model. METHOD(S): Here we present a method – kernel Electrical Source Imaging (kESI) – of reconstruction of the activity underlying the measured potentials. kESI allows us to use information from arbitrarily placed electrodes and may integrate patient-specific anatomical information which increases precision of localization of epileptogenic zone for a specific patient. RESULTS: The preliminary results are promising. The major advantage of kESI over previous work is that it accounts for spatial variations of brain conductivity and can take into account patient-specific brain and skull anatomy. CONCLUSIONS: Nevertheless, further work is necessary to bring this method to the level of clinical application. FINANCIAL SUPPORT: Project funded from the Polish National Science Centre’s OPUS grant (2015/17/B/ ST7/04123).