A new, meshfree method employing the node-based, smoothed point interpolation method (NS-PIM) is presented as an alternative to the nonlinear finite-element approach for concrete members. The nonlinear analysis is replaced by sequentially linear analyses (SLA), and a smeared, fixed concrete cracking model was used. A notched concrete beam was employed for validation. Using a crack band width factor of 2.0 and 10-mm nodal spacing, the peak load differed by only 3.5% from experimental results. Overall results were similar to experimental ones, as well as to those published by researchers using finite-element SLA. The approach provides two major advantages over finite-element-based SLA: (1) nodal distortion insensitivity, and (2) nodal spacing insensitivity.