In　this　paper,　the　problem　of　reachable　set　estimation　of　multi-agent　systems　(MASs)　is　investigated.　For　the　ease　of　application,　balanced　communication　topology　with　a　directed　spanning　tree　and　non-zero　initial　condition　are　considered.　Based　on　the　Lyapunov　method　and　orthogonal　transformation　technique,　sufficient　conditions　are　established　in　terms　of　linear　matrix　inequalities　to　guarantee　that　the　reachable　set　of　MASs　is　bounded　by　a　compact　ellipsoid.　Moreover,　by　employing　some　useful　skills　from　stochastic　analysis,　the　result　is　then　extended　to　the　problem　for　MASs　under　Markovian　switching　topologies.　The　effectiveness　of　the　obtained　results　is　illustrated　by　two　numerical　examples.　©　2020