We develop several Euclidean numerical radius bounds for the product of two d-tuple operators using positivity criteria of a 2×2 block matrix whose entries are d-tuple operators. From these bounds, by using polar decomposition of operators, we obtain Euclidean numerical radius bounds for d-tuple operators. Among many other bounds, it is shown that (Formula presented.) where we(A) and ‖A‖ are the Euclidean numerical radius and the Euclidean operator norm, respectively, of a d-tuple operator A=(A1,A2,…,Ad). Further, we develop an upper bound for the Euclidean numerical radius of an n×n operator matrix whose entries are d-tuple operators. In particular, it is proved that if [Aij]n×n is an n×n operator matrix then (Formula presented.) where each Aij is a d-tuple operator, 1≤i,j≤n, aij=we(Aij) if i=j, aij=we(|Aji|+|Aij∗|)we(|Aij|+|Aji∗|) if ij. Some related applications are also discussed.