We describe an approach for the construction of singular solutions to the 3D Euler equations for complex initial data. The approach is based on a numerical simulation of complex traveling wave solutions with imaginary wave speed, originally developed by Caflisch for axisymmetric flow with swirl. Here, we simplify and generalize this construction to calculate traveling wave solutions in a fully 3D (nonaxisymmetric) geometry. Our new formulation avoids a numerical instability that required the use of ultra-high precision arithemetic in the axisymmetric flow calculations. This is joint work with Russ Caflisch.