Elvius presided over 25 dissertations in astronomy, and
published many almanacs, was also interested in calender calculations.
He had ideas on constructing a planetarium ("Machina astronomica") as early as 1704.
Published calculations of the comet of 1715.
One of the founders of "Collegium Curiosum" (1710), the embryo of what later became
the Royal Society of Sciences in Uppsala, the first scientific academy in Sweden.
Elvius was the first in Sweden to lecture on Kepler´s laws.
He published the first tables of logartihms in Sweden: Tabula compendiosa logarithmorum sinuum
ad quadrantes gradus. (1698)
A widely used popular book in Swedish on the practical use of the quadrant:
En kort undervisning om den astronomiske kvadrants nytta och bruk. (1697), which was reprinted
in many editions during the 18th century, was written by him.
In his publication De causis motuum caelestium (1716) Elvius critically examined Newton´s law of
gravitation, beeing himself a follower of the opposing "whirlpool" theory of Descartes.