Implementing a 1D stencil code via SIMD instructions on a computer with vector registers having N processing elements (PEs), among them a set of coefficient vector registers, a set of at most N data vector registers, and a set of result vector registers. The M stencil coefficients are loaded in a particular pattern into M+N−1 coefficient vector registers. Successive sets of N consecutive data values are received, and each data value of a set is loaded into all PEs of a data vector register of the set of data vector registers. The result vector registers accumulate sums of products of consecutive coefficient vector registers with corresponding data vector registers. The contents of any result vector register containing a sum of all coefficient vector register-data vector register products is output, and the result vector register is reused for accumulating.