as indicated before the material will be soluble in HCl (if it is gypsum). The digestion of gypsum is easily done (finely powdered) by using e.g. 0,1 g sample by adding 5 mL HCl (30 %; or higher)). You can observe the solution process immediately when adding the acid stepwise (under fume hood) to sample. In addition, your description of digest results indicate that your sample is not gypsum (CaSO4 . 2 H2O). It could also be anhydrite(CaSO4) or some type of industrially burnt gypsum (half-hydrate, dead burnt gypsum (?)) which by adding of water (or diluted acid) will show some setting. Also these compounds are soluble in HCl. Possibly the acidity of your HCl was too low or you took too much sample. You have to try out by going to the concentrated side of HCl and to minimise the sample amount. In case of non-gypsum sulphates you need some more or higher concentrated acid. In these cases the solution process could also take more time - but it should work. To speed up the trials you also could bring some small sample amount to a mortar, add carefully a successively increasing amount of conc acid (fume hood) and grind with pestle to observe the solution process.
A final remark: solutions high in Ca-sulfate tend to clock slowly the nozzles of nebulisers (AAS, ICP) due to hidden supersaturation under nebulizing conditions. So you should prefer high dilutions, which due to high Ca-sensitivity of AAS or ICP is necessary anyway. Also, you should check state of the instrument (state of nebuliser) during analysis runs by aspirating control solutions with defined conc, which hopefully yield reproducible signals. Otherwise you have to clean by prolonged aspirating of pure acid, alternating with water, until you reach a stable zero-signal.
Many many thanks Dieter for this perfect guide. As you recommend, I add 5 to 10 cc HCl 0.37 to 0.1 gr sample and heat it for ~45 min. It got completely solved and the Ca percent we obtained is very close to Ca% in the ideal formula.
For a somewhat related discussion ― yet on the distinct purpose of surface cleaning from CaSO4/MgSO4 scale: https://www.researchgate.net/post/What_is_the_solution_to_dissolve_the_scale_of_CaSO4_and_MgSO4_from_RO_membrane_surface