An interfolding machine produces interfolded sheets according to an interfolding configuration and, starting from a web of paper provides a feeding section, which applies a tension on the web and moves the same along a feeding direction feeding the same to a cutting section, in which the web of paper is cut into a series of sheets at a cutting point between a cutting roller and a counter-cutting element. Downstream of the cutting section, a folding section includes a first and a second folding rollers counter-rotating with respect to each other. The first and second folding rollers rotate about respective rotation axes with a first peripheral velocity vP, and fold, at a folding zone, a plurality of sheets in a plurality of panels and form the stack of interfolded sheets. The cutting roller alternately distributes the aforementioned sheets between a transfer roller and the first folding roller.