Understanding Mesh Analysis
Your mesh currents are wrong. These are the correct equations:

$$\begin{align}
I_1R_1+(I_1-I_3)R_3+(I_1-I_2)R_2&amp;=0\\
(I_2-I_1)R_2+(I_2-I_3)R_4&amp;=15V\\
(I_3-I_2)R_4+(I_3-I_1)R_3&amp;=21V
\end{align}$$

Solving this system gives the following mesh currents:

$$\begin{align}
I_1&amp;=18.000\,A\\
I_2&amp;=21.545\,A\\
I_3&amp;=20.818\,A
\end{align}$$

All currents in the network can be calculated from these mesh currents, and the results correspond to the ones obtained by Multisim, e.g. the current through \$R_2\$ is \$I_2-I_1=3.5455\,A\$.