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The model describing asymmetrical compression of high-aspect-ratio laser-fusion shells under conditions of non-uniform illumination is proposed. Thin-shell approximation is used as a base. Motion equations of a thin shell are solved numerically by code "SOM". The asymmetry being brought during acceleration phase is characterized by asymmetry function introduced taking into account thermal conduction smoothing of energy deposition in corona, and is set as initial conditions. Analytic solution of small three-dimensional perturbations growth problem is derived. It gives a good estimation of compression losses even for large amplitude and for several modes superposition case. The analysis of experiments conducted on the SOKOL, OCTAL, OMEGA facilities is given. The model represents a good agreement with experimental data: degradation of DT-fuel compression and neutron yield falling can be explained by large scale asymmetry appearance due to target illumination non-uniformity.