The numerical range and numerical radius of some model operators are investigated. Among other things, a complete description of the numerical range of square-zero operators on Hilbert spaces, including the skew-symmetric Volterra operator (V(0)f) (x) = integral(x)(-x)f(t)dt on the Lebesgue space L(2) (-1, 1), is also given. (C) 2010 Elsevier Inc. All rights reserved.