LIPSS (Laser Induced Periodic Surface Structure) formation on copper thin films induced by a picosecond laser beam (Nd:YAG laser at 266 nm, 42 ps and 10 Hz) was studied experimentally. Copper thin films were deposited on glass and silicon substrates by magnetron sputtering. The surface modifications of irradiated zones were analyzed by scanning electron microscopy. Two distinct types of LIPSS were identified with respect to the laser fluence (F), number of laser shots (N) and substrate material. Namely, with a number of laser shots (1000 < N < 10,000) and a fluence of (200 mJ/cm2 < F < 500 mJ/cm2), Low Spatial Frequency LIPSS (LSFL with a spatial period of Λ ∼ 260 nm and an orientation perpendicular to polarization) and High Spatial Frequency LIPSS (HSFL with a spatial period of Λ ∼ 130 nm and an orientation parallel to the polarization) were observed. The regime of regular spikes formation was determined for N ≥ 1000. Moreover, the 2D-map of the relationship among LIPSS formation, laser fluence and number of laser shots on copper thin film with two different substrates was established. A physics interpretation of regular spikes and LIPSS formation on copper thin film induced by ps laser with overlapping multi-shots is proposed based on experimental data and the theory of Plateau-Rayleigh instability.