In designing targets for laboratory long-rod penetration tests, the question of lateral confinement often arises, "How wide should the target be to exert enough confinement?" For ceramic targets, the problem is enhanced as ceramics are usually weak in tension and therefore have less self-confinement capability. At high velocities the problem is enhanced even more as the crater radius and the extent of the plastic zone around it are larger. Recently we used the quasistatic cavity expansion model to estimate the resistance of ceramic targets and its dependence on impact velocity [1]. We validated the model by comparing it to computer simulations in which we used the same strength model. Here we use the same approach to address the problem of lateral confinement. We solved the quasistatic cavity expansion problem in a cylinder with a finite outside radius "b" at which σr (b) = 0 (σr = radial stress component). We did this for three cases: ceramic targets, metal targets, and ceramic targets confined in a metal casing. Generally, σr (a) is a decreasing function of "a" ("a" = expanding cavity radius, and σr (a) = the stress needed to continue opening the cavity). In the usual cavity expansion problem b → ∞, σr (a) = const., R =-σr (a) (R = resistance to penetration). For finite "b" we estimate R by averaging σr (a) over a range o ≤ a ≤ ar, (where ar, the upper bound of the range, is calibrated from computer simulations). We ran 14 computer simulations with the CTH wavecode and used the results to calibrate ar for the different cases and to establish the overall validity of our approach. We show that generally for Dt Dp > 30, the degree of confinement is higher than 95% (Dt = target diameter; Dp = projectile diameter; and degree of confinement = R R∞; R∞ = resistance of a laterally infinite target). We also show the tensile strength of ceramic targets (represented by the spall strength Pmin) has a significant effect on the degree of confinement, while other material parameters have only a minor effect. © 1995.