Life cycle analysis (LCA) is a popular tool for determining the environmental impacts of a product in use. The aim of this study is to carry out a life cycle analysis, gate-to-gate, of a mass packaging process using a polyethylene shrinking film with a focus on energy consumption, raw material use and associated emissions, and film post-consumer disposal scenarios. Two different scenarios for the disposal of the shrinking film used in the packaging process were analyzed, namely recycling and landfills. The analysis showed that choosing recycling as the post-consumer management of film waste within the studied system boundaries reduces the negative environmental impact by approximately 17%. The study showed significantly higher environmental benefits in terms of harmfulness to human health for recycling than for landfills. A study of the environmental impact of the mass packaging process depending on the energy source showed that using a renewable source minimizes environmental damage. Three sources of energy options were analyzed, including the country’s energy mix, wind, and solar. The research shows that changing sources to wind power reduces potential damage to human health by 91%, to ecosystems by 89%, and to resources by 92% compared to the country’s energy mix power option. When comparing the results for the renewable energy options, the variant with energy from wind presents lower harm in all three damage categories compared to the solar option.