With an improved algebraic mesh-deforming algorithm, STAR-CD, a commercial computational fluid dynamics (CFD) solver is employed for the numerical analysis of a transonic oscillating linear cascade of advanced design blades. The center blade oscillates 0.6-degrees about the middle cord. The numerical simulation is conducted for a frequency range from 200 Hz to 500 Hz. A hybrid grid, which utilizes a structured O-grid around the airfoil and an unstructured grid everywhere else is employed. The Spalart-Allmaras (S-A), one equation turbulence model, along with other two equation k-ε models, are also utilized for the steady state simulation. The S-A turbulence model provided significantly better steady state results in the separated flow region than the k-ε model. The agreement between the experimental data and CFD prediction was better for the M=0.8 unsteady results than the M=0.5 on the suction surface. This could be attributed to a larger unsteady variation in the reattachment location for the M=0.5 results than the M=0.8. Finally, the time average of the unsteady skin friction coefficient is significantly different than the steady state value indicating nonlinear unsteady aerodynamics are significant for this analysis.