MuST: the multilevel sinc transform. A fast multilevel algorithm (MuST) for evaluating an n-sample sinc interpolant at mn points is presented. For uniform grids, its complexity is 25mnlog(1/δ) flops for the sinc kernel and 75mnlog(1/δ) for the sincd kernel, where δ is the target evaluation accuracy. MuST is faster than fast Fourier transform- and fast multiple method-based evaluations for large n and/or for large δ. It is also applicable to nonuniform grids and to other kernels. Numerical experiments demonstrating the algorithm’s practicality are presented.