Beam-like　structures　are　widely　used　in　engineering.　The　accuracy　of　the　analytical　mode　shapes　of　these　structures　is　important　for　studying　their　dynamic　characteristics.　A　method　is　presented　in　this　study　to　theoretically　obtain　and　quantitatively　validate　the　analytical　mode　shapes　of　a　beam-like　structure　with　a　Z-shaped　configuration.　The　governing　equations　and　boundary　conditions　of　the　structure＇s　planar　motion　are　derived　using　Hamilton＇s　principle.　Frequencies　and　analytical　mode　shapes　of　the　structure　are　theoretically　obtained　and　compared　with　the　numerical　results　from　finite　element　method.　The　comparison　of　frequencies　and　modal　assurance　criterion　is　used　to　quantitatively　validate　the　analytical　mode　shapes.　Examples　are　presented　to　show　the　analytical　mode　shapes　of　Z-shaped　beams　with　different　fold　angles.　The　proposed　method　is　useful　for　improving　the　accuracy　of　analytical　mode　shapes＇　which　is　beneficial　to　the　design　and　control　of　beam-like　structures　in　engineering　fields.