What type of bond allows metals to be flattened and shaped?

Metallic bond

Metals are bound together by metallic bonds characterized by the sharing of free electrons among a lattice of the metal ions. This type of bonding gives metals unique properties such as strength, ductility, malleability, electrical and thermal conductivity, opacity, and luster. 

This property of metal to be flattened and shaped is called malleability. When stress is applied to the metal, its atoms merely roll or slide over each other into new positions while keeping the metallic bond intact. The bonds do not break, thereby allowing the metal to be flattened out instead of crumbling or breaking into pieces.