The asperities of rough surfaces have long been considered to be points higher than their immediate neighbors. Based on this concept, theories were developed for quantitatively understanding the elastic and plastic nature of contact between rough surfaces. Recently it has been recognized that the above model for asperities is inadequate. Consequently, all the models that have been constructed based on that model are inadequate too. In this paper, based on a newly developed multiple-point asperity model, the elastic and plastic contact problem between nominally flat surfaces is reformulated. This leads to finding the deformed area, and load produced by the contact. The model is developed for the general form of isotropic rough surfaces with arbitrary height distribution and autocorrelation function (ACF). The microcontact areas generated by each asperity contact are considered to be circles. The Gaussian distribution of heights and exponential ACF are considered as a benchmark to compare the results of the new model with the existing models. Using results from numerical models developed by other groups, the new model is validated.