In this paper, investigation of radiation properties of the traveling-wave sinusoidal wire antennas is extended to the millimeter-wave frequencies (Ka-band) for the antennas whose geometrical dimensions vary in a wide range. Far-field patterns and S-parameters of composed three antenna sets were measured. A mathematical model was constructed for the structure and a MATLAB code based on this theoretical approach was written to calculate patterns, phase and attenuation constants of all investigated antennas. Frequency characteristics and the relation of antenna dimensions with wave parameters were investigated. Measured and calculated patterns were also compared with the constructed far-field patterns obtained by MoM (method of moments) and the MoM current distributions were used to explain the loss mechanisms of antennas. A directive, undistorted and smooth radiation can be achieved only choosing small undulated antennas whose peak-to-peak amplitude to period ratio kappa is smaller than 0.4 (kappa < 0.4). It is shown that wavelength of broadside radiation is not equal to antenna period for all antennas, except for very small undulated antennas (kappa < 0.2). This antenna type can be used as a frequency-scan antenna for millimeter wave radars.