A tearable core, adapted for winding a sheet product, includes a cylindrical body wall defining a longitudinal hole of longitudinal axis XX′. The cylindrical body wall is tearable from an edge, and includes an outer strip and an inner strip that are helically wound on one another and displacedly overlapped in a lateral direction parallel to the longitudinal axis XX′, and secured together through their mutually facing surfaces by a first region of attachment. The strips are made of the material having characteristics such that the inner strip and the outer strip are made of cardboard having different water drops. The cylindrical body wall is formed by securing together the outer strip, a first end part of the outer strip of one turn being superposed and secured to a second end part of the outer strip of an adjacent turn through their mutually facing surfaces by a second region of attachment.