Abstract: A method for manufacturing cold rolled, nondirectional electrical steel sheets and strips having a high magnetic flux density wherein a molten steel is solidified to obtain a slab in a manner that columnar grains develop predominantly from the surface in the direction of thickness of the slab up to a depth of more than 50%; said slab is heated to a temperature above 1000.degree.C without cogging and rolling to form .gamma.-phase at least more than about 10% of said slab, and hot rolled strongly with a draft of more than 98% without reheating to obtain a hot rolled steel sheet; and said hot rolled steel sheet is cold rolled with a draft of 64 - 84%, heated with a heating velocity of more than 1.6.degree.C/sec., and annealed at a temperature of 600.degree. - 1200.degree.C.