A new insight into capillary channel formation with a high aspect ratio in the translucent matter by nanosecond UV laser pulses is discussed based on our experiments on KrF laser multi-pulse drilling of polymethyl methacrylate and K8 silica glass. The proposed mechanism includes self-consistent laser beam filamentation along a small UV light penetration depth caused by a local refraction index increase due to material densification by both UV and ablation pressure, followed by filamentation-assisted ablation. A similar mechanism was shown to be realized in highly transparent media, i.e., KU-1 glass with a multiphoton absorption switched on instead of linear absorption. Waveguide laser beam propagation in long capillary channels was considered for direct electron acceleration by high-power laser pulses and nonlinear compression of excimer laser pulses into the picosecond range.