The article contains a presentation of the basic models methods and measures used to determine the risk of insolvency of an insurance company. The topics discussed include the solvency margin, risk-based capital and the probability of ruin. The concept of a scale of safety is introduced; this allows the extent of the risk involved in the activities of the insurance company to be expressed in terms of capital requirement. A method for calculating the extended solvency margin (ESM) is proposed. The model of risk-based capital (RBC) is presented in the standard version, using fixed RBC coefficients. The probability of ruin (risk of insolvency) in an annual time-frame has been determined using analytical methods and simulations. The theoretical discussion is illustrated with empirical examples derived from the activities of non-life insurance companies operating as joint stock companies in Poland in the period 1995-2002.