In the paper, the following stochastic differential equation \[ d X(t) = f(X(t),i)dt+g(X(t),i)dw(t), \quad 1\leq i\leq N, \tag{1} \] with the initial condition \[ \qquad X(0)= x\in \mathbb{R}^{d} \tag{2} \] is considered. In (1)-(2), \(\mathcal{M}=\left\{ 1,2,3,\ldots,N \right\}\), \(f:\mathbb{R}^{d}\times\mathcal{M}\to \mathbb{R}^{d}\) and \(g:\mathbb{R}^{d}\times\mathcal{M}\to \mathbb{R}^{d\times d}\). The authors study the stochastic invariance for a class of equations (1)--(2). The invariance is understood as follows. A closed subset \(\mathcal{D}\subset \mathbb{R}^{d}\) is said to be stochastically invariant with respect to eq.~(1) if, for all \(x\in \mathcal{D}\), there exists a weak solution \((X,W)\) of eq.~(1) starting at \(X(0)=x\) such that \(X(t)\in \mathcal{D}\) almost surely for all ~\(t\geq 0\). The authors supply the necessary and sufficient conditions for the invariance of closed sets of \(\mathbb{R}^{d}\). The main results are formulated in Theorem 3.1. The coefficients \(f\) and \(g\) are non-Lipschitz and satisfy the linear growth condition. Moreover, \(\mathcal{C}:=g\, g^{T}\) is assumed to be extended to a \(C^{(1,1)}_{\mathrm{loc}}(\mathbb{R}^{d},\mathbb{S}^{d})\) function on \(\mathcal{D}\). Here, \(\mathbb{S}^{d}\) stands for the cone of symmetric \(d\times d\) matrices. The stochastic invariance of the equation (1) is investigated by using the martingale property and positive maximum principle. The paper is well and clearly written. It should be interesting for people working in stochastic equations.