Let \((\Omega,{\mathcal F},P)\) be a complete probability with a right-continuous increasing family \(({\mathcal F_t})_{t\geq 0}\) of \(\sigma\)-fields each containing all \(P\)-nul sets. Let \(B= (B_t)_{t\geq 0}\) be an \(r\)-dimensional \(({\mathcal F}_t)\)-Brownian motion. The author considers the following stochastic differential inclusion \[ dX_t\in \sigma(t, X_t)\, dB_t+ b(t, X_t)\,dt,\tag{1} \] where \(\sigma: [0,T]\times \mathbb{R}^d\to P(\mathbb{R}^d\otimes \mathbb{R}^d)\), \(b:[0,T]\times \mathbb{R}^d\to P(\mathbb{R}^d)\) are set-valued maps. The study of the existence and properties of solutions of these stochastic differential inclusions have been developed by \textit{N. V. Ahmed} (1994), \textit{A. A. Levakov} [Differ. Equations 34, No. 2, 208--214 (1998; Zbl 1026.60505)] and others. Also the results for the viable solutions have been made by \textit{J.-P. Aubin} and \textit{G. Da Prato} [ Stochastic Anal. Appl. 16, No. 1, 1--15 (1998; Zbl 0931.60059) and \textit{B. Truong-Van} and \textit{X. D. H. Truong} [ibid. 17, No. 4, 667--685 (1999; Zbl 0952.60055)]. For the stochastic differential equation associated with (1), the results for the existence, uniqueness and properties of solutions have been done under various conditions that \(\sigma\) and \(b\) are continuous and bounded or Lipschitzian or Hölder continuous [see \textit{N. Ikeda} and \textit{S. Watanabe}, ``Stochastic differential equations and diffusion processes'' (1981; Zbl 0495.60005)]. The author proves the existence of solution for stochastic differential inclusion (1) under the condition that \(\sigma\) and \(b\) satisfy the local Lipschitz property and linear growth [see \textit{Y. S. Yun} and \textit{I. Shigekawa}, Far East J. Math. Sci. (FJMS) 7, No. 2, 205--212 (2002; Zbl 1029.60009)]). In this note the author proves that any solution for the stochastic differential inclusion (1) is bounded. In the second part of the paper, ``Preliminaries'', the author prepares the definition of solution of stochastic differential equation and selection theorems. The last part ``Main results'' contains the most famous continuous selection theorem [\textit{J.-P. Aubin} and \textit{A. Cellina}, ``Differential inclusions: Set-valued maps and viability theory'' (1984; Zbl 0538.34007)]: Let \(X\) be a metric space, \(Y\) a Banach space. Let \(F\) from \(X\) into the closed subsets of \(Y\) be lower semicontinuous. Then there exists \(f: X\to Y\), a continuous selection from \(F\).