Auctions are important market mechanisms for the allocation of goods and services. In the paper a complex trading model is proposed. The proposed model, called multidimensional auction, is a generalization of an LP model of standard single item English auction. Multidimensional auctions include the possibility of auction generalization for multi-item, multi-type, multi-round and multi-criteria. The multi-item model for multi-type auction is modelled and solved by multi-round approach with multiple criteria. The proposed model illustrates the possibility to formulate and solve multidimensional auctions as mathematical programming problems. Allowing bidders more fully to express preferences leads to improved economic efficiency and greater auction revenue.