Parallel　kinematic　machines　(PKMs)　have　been　proposed　as　an　alternative　solution　for　high-speed　machining　(HSM)　tool　for　several　years.　However,　their　dynamic　characteristics　are　still　considered　an　issue　for　practice　application.　Considering　the　three　prismatic-revolute-spherical　(3-PRS)　PKM　design　as　a　typical　compliant　parallel　device,　this　paper　applies　substructure　synthesis　strategy　to　establish　an　analytical　elastodynamic　model　for　the　device.　The　proposed　model　considers　the　effects　of　component　compliances　and　kinematic　pair　contraints　so　that　it　can　predict　the　dynamic　characteristics　of　the　3-PRS　PKM.　Based　on　eigenvalue　decomposition　of　the　characteristic　equations,　the　natural　frequencies　and　corresponding　vibration　modes　at　a　typical　configuration　are　analyzed　and　verified　by　numerical　simulations.　With　an　algorithm　of　workspace　partitions　combining　with　eigenvalue　decompositions,　the　distributions　of　lower-order　natural　frequencies　throughout　the　workspace　are　computed　to　reveal　a　strong　dependency　of　dynamic　characteristics　on　mechanism＇s　configurations.　In　addition,　the　effects　of　the　radii　of　the　platform　and　the　base　along　with　the　cross　section　of　the　limb　on　lower-order　natural　frequencies　are　analyzed　to　provide　useful　information　during　the　early　design　stage.　At　last,　frequency　response　analysis　for　the　tool　center　point　(TCP)　is　worked　out　based　on　the　elastodynamic　model　to　provide　primary　guideline　for　cutting　chatter　avoidance.