This text describes wide variety of models for IBNR reserve estimation, among them we can find chain ladder, Munich chain ladder, Cape Cod or regression methods. Especially, it aims at identification of model assumptions, its verification, impacts of their non-fulfillment and resulting model modification. Moreover, this work deals with anomalies and specificity of historical data and tries to suggest solutions for this problems. The last part of the thesis is dedicated to real analysis of motor third party liability.