When analyzing the reliability of the multistate system (MSS), there always are multiple types of uncertainties in the MSS. For example, in some complex systems, due to the differences of the sample amount, some information are random, and some information is only given as intervals since a lack of samples. An multiple state reliability analysis method based on evidence universal generating function (EUGF) to handle MSS containing multiple type uncertainties is proposed. This method based on the evidence theory, and the evidence theory has good quantification ability of epistemic uncertainty such as interval information, experts information, and it could make full use of such uncertainty information in engineering. The EUGF provides two measures of belief and plausibility for reliability evaluation of MSS, thus it could improve the incredibility of the reliability results of the MSS including imprecise information. For the MSS containing hybrid uncertainties of intervals and random uncertainty, first the random uncertainties are divided into discrete intervals. Then the uniform EUGF model for hybrid uncertainties is built. Finally, the reliability of MSS is analyzed based on the EUGF. Some cases are illustrated to verify the EUGF method.