A lattice model of proteins is introduced. "A protein molecule" is a chain of nown-intersecting units of a given length on the two-dimensional square lattice. The copolymeric character of protein molecules is incorporated into the model in the form of specificities of inter-unit interactions. This model proved most effective for studying the statistical mechanical characteristics of protein folding, unfolding and fluctuations. The specificities of inter-unit interactions are shown to be the primary factors responsible for the all-or-none type transition from native to denatured states of globular proteins. The model has been studied by the Monte Carlo method of Metropolis et al., which is now shown applied to approximately simulating a kinetic process. In the strong limit of the specificity of the inter-unit interaction the native conformation was reached in this method by starting from an extended conformation. The possible generalization and application of this method for finding the native conformation of proteins form their amino sequence are discussed.