Let \((H,\circ)\) be a finite hypergroupoid and associate to \(H\) the family of subsets of \(H\) \[ {\mathcal B} = \{x\circ y\mid (x,y) \in H^ 2\} = \{X_ 1^{(n_ 1)},\dots,X_ s^{(n_ s)}\} \] where the exponents in brackets denote the multiplicities. \((H,{\mathcal B})\) is a block design and it is called the design associated to \((H,\circ)\). A hypergroupoid \((H,\circ)\) is called a 2-\((v,k)\) hypergroupoid if its associated design is a 2-\((v,k,\lambda)\) design (in this case \(\lambda\cdot (v-1) = v\cdot k\cdot (k-1))\). Necessary conditions on the values of the parameters \(v\), \(k\) for the existence of 2-\((v,k)\) hypergroupoids are given in Section 2 of the paper. In Sections 3 and 4 some particular cases for \(v\) and \(k\) are studied. These cases lead respectively to hypergroupoids associated to projective planes or to hypergroupoids associated to some trivial designs.