Let A = (A 1 , . . . , A m ) be an m-tuple of bounded linear operators acting on a Hilbert space H. Their joint (p, q)-matricial range Λ p,q (A) is the collection of (B 1 , . . . , B m ) ∈ M m q , where I p ⊗ B j is a compression of A j on a pq-dimensional subspace. This definition covers various kinds of generalized numerical ranges for different values of p, q, m. In this paper, it is shown thaton a closed subspace of H, and consider the joint essential (p, q)-matricial range Λ ess p,q (A) = {cl(Λ p,q (A 1 + F 1 , . . . , A m + F m )) : F 1 , . . . , F m are compact operators}.Both sets are shown to be convex, and the latter one is always non-empty and compact.Keywords: Joint matricial range, Joint essential numerical range, Higher rank numerical range, Bounded linear operators 2010 MSC: 47A12, 47A13, 47A55, 15A60