The stability of copolymer tethers is investigated theoretically. Self-assembly of diblock or triblock copolymers can lead to tubular polymersomes which are known experimentally to undergo shape instability under thermal, chemical and tension stresses. It leads to a periodic modulation of the radius which evolves to assembly-line pearls connected by tiny tethers. We study the contributions of shear surface viscosity and spontaneous curvature and their interplay to understand the pearling instability. The performed linear analysis of stability of this cylinder-to-pearls transition shows that such systems are unstable if the membrane tension is larger than a finite critical value contrary to the Rayleigh-Plateau instability, an already known result or if the spontaneous curvature is in a specific range which depends on membrane tension. For the case of spontaneous curvature-induced shape instability, two dynamical modes are identified. The first one is analog to the tension- induced instability with a marginal mode. Its wavenumber associated with the most un- stable mode decreases continuously to zero as membrane viscosity increases. The second one has a finite range of unstable wavenumbers. The wavenumber of the most unstable mode tends redto be constant as membrane viscosity increases. In this mode, its growth rate becomes independent of the bulk viscosity in the limit of high membrane viscosity and behaves as a pure viscous surface.