Let Ω ⊂ Rn be an open and bounded set with the smooth boundary ∂Ω. Consider the following initial boundary value problem for the plate equation, which in what follows will be called (Pε):   εutt(x, t) + ut(x, t) + Δ2u(x, t) + B(u(t)) = f(x, t), (x, t) ∈ Ω × (0,T) u t=0 = u0(x), ut t=0 = u1(x), x∈ Ω u x∈∂Ω = ∂u ∂¯ν x∈∂Ω = 0, t≥ 0, (Pε) where ¯ν is the outer normal vector to ∂Ω and ε is a small positive parameter. We study the behaviour of the solutions to the problem (Pε) relative to the corresponding solutions to the unperturbed problem:   vt(x, t) + Δ2v(x, t) + B(v(t)) = f(x, t), (x, t) ∈ Ω × (0,T) v t=0 = u0(x), x∈ Ω v x∈∂Ω = ∂v ∂¯ν x∈∂Ω = 0, t≥ 0, (P0) as ε → 0. We consider the case when the operator B is Lipschitz and the case when the operator B is monotone.Under some conditions on u0,u1 and f we prove that u → v in C([0,T];L2(Ω)) ∩ L∞(0,T;H2(Ω)), as ε → 0. (1) This means that in the indicated norms the perturbation (Pε) of the system (P0) is regular. Moreover, we prove that u′−v′−αe−t/ε → 0 in C([0,T];L2(Ω))∩L∞(0,T;H2(Ω)) α ̸= 0, (2) as ε → 0. It means that the derivatives of solutions to the problem (Pε) does not converge to the derivatives of the corresponding solutions to problem (P0), as ε → 0. The relation (2) shows that the derivative u′ has a singular behaviour in the neighborhood of t = 0 as ε → 0. This singular behaviour is determined by the function αe−t/ε, which is the boundary layer function, and the neighborhood of t = 0 is the boundary layer for u′. The proofs of the relations (1) and (2) are based on two key points. The first one is the relationship between the solutions to the problems (P0) and (Pε) in the linear case. The second key point are the a priori estimates of the solutions to the problem (Pε), which are uniform relative to the small parameter ε.