In　this　paper,　we　compare　the　Differential　transformation　method　and　Adomian　decomposition　method　to　solve　Euler-Bernoulli　Beam　vibration　problems.　The　natural　frequencies　and　mode　shapes　of　the　clamped-free　uniform　Euler-Bernoulli　equation　are　calculated　using　the　two　methods.　The　Adomian　decomposition　method　avoids　the　difficulties　and　massive　computational　work　inherent　in　Differential　transformation　method　by　determining　the　very　rapidly　convergent　analytic　solutions　directly.　We　found　the　solution　between　the　two　methods　to　be　quite　close.　According　to　calculation　of　eigenvalues,　natural　frequencies　and　mode　shapes,　we　compare　the　convergence　of　Differential　transformation　method　and　Adomian　decomposition　method.　The　two　methods　can　be　alternative　ways　to　solve　linear　and　nonlinear　higher-order　initial　value　problems.