In the paper drying process is used the most part of the thermal energy necessary papermaking. In this paper it is presented a mathematical model to optimize of this process and the general architecture of the computer program developed. Paper is generally dried in a multi-cylinder dryer section, in which the continuous paper web is heated as it passes internally steam-heated dryer cylinders. The mathematical model of the paper drying process that is included in the optimization model considers the heat transfer in a porous sheet during drying and in the cylinder shell. The mass transfer is considered only into the boundary conditions at the paper surface. The unsteady state equations are solved by means of a numerical technique – finite element method. Using finite elements, the differential analytical model is transformed in a numerical model. Computer solves this model. In the optimization model there are eight independent variables: machine speed, basis weight, initial moisture content of paper web, felt tension, steam pressure in the heating battery of air, steam pressure in the dryer cylinders, exhaust air flow from machine hood and air flow blow to the hall ceiling. The dependent variables, which are determined from differential equations of the heat transfer, are sheet temperature and dryer surface temperatures. The objective of the optimization model is the minimization of the paper cost subject to the operation and constructive constraints. It is considered the component of the cost that depends on the thermal specific consumption namely unitary thermal cost of paper. A computer program was developed based on the optimization model. This program is composed from a main program and seven programs called from it and database. The optimization model was applied for two paper machines. Its numerical results are presented in this paper, too.