Sodium-alginate (SA) based nanofluids represent a new generation of fluids with improved performances in terms of heat transfer. This work examines the influence of the nanoparticle shape on a non-Newtonian viscoplastic Cu-nanofluid pertaining to this category. In particular, a stretching/shrinking sheet subjected to a transverse magnetic field is considered. The proposed Cu-nanofluid consists of four different nanoparticles having different shapes, namely bricks, cylinders, platelets, and blades dispersed in a mixture of sodium alginate with Prandtl number Pr = 6.45. Suitable similarity transformations are employed to reduce non-linear PDEs into a system of ODEs and these equations and related boundary conditions are solved numerically by means of a Runge-Kutta-Fehlberg (RKF) method. Moreover, analytical solutions are obtained through the application of a MAPLE built-in differential equation solver (Dsolve). The behavior of prominent parameters against velocity and temperature is analyzed. It is found that the temperature increases for all shapes of nanoparticles with the viscoplastic parameter and the Eckert number.