Shell structures with a mid surface of helicoid shape find application in many technical fields, mostly in civil and mechanical engineering. There is a variety of helicoid shells, but the most well-known and used are two types of ruled helicoids: right and oblique. The article is devoted to analytical and numeric-analytical methodologies for shallow right and oblique helicoids. The general approach is based on Kirchhoff–Love linear theory of thin elastic shells. Analytical results can be used for preliminary design and calculations aimed at the understanding of construction physics and regularities of stress-strain state behavior. Two methodologies of stress-strain analysis are presented: the analytical method for shallow right helicoid, and the numeric-analytic method for oblique helicoid (including any special or degenerated case). The numerical results are verified. The results and approach outlined could be of interest to designers and scientists, who want to understand the generalities of thin ruled helicoid shell behavior.