This paper presents the Extended Force Density Method which allows for form-finding of cable nets under self-weight. Formulation of the method is based on the curved catenary cable element which assures high accuracy of the results and enables solving wide range of problems. Essential rules of the Force Density Method (FDM) are summarized in the paper. Some well-known formula describing behaviour of a catenary cable element under self-weight are given.Next the improved variant ofFDMwith all the theoretical and numerical details is introduced. Iterative procedure for solving nonlinear equations is described. Finally a simple verification example proves correctness of methods assumptions. Two further analyses of parameters crucial for correct use of Extended Force Density Method (EFDM) are presented in order to indicate their initial values for other numerical examples. Accuracy of the results are also investigated. A computer program UC-Form was developed in order to perform the calculations and graphically present the results. Some examples of use of EFDM are presented in details in Part II – Examples of application.