This work aims at developing a generic and anisotropic point error model, which is capable of computing magnitude and direction of a priori random errors, described in the form of error ellipsoids for each individual point of the cloud. The direct TLS observations are the range (ρ), vertical (α) and horizontal (θ) angles, each of which is in fact associated with a priori precision value. A practical methodology was designed and performed in real-world test environments to determine these precision values. The methodology has two experimental parts. The first part is a static and repetitive measurement configuration for the determination of a priori precisions of the vertical (σα) and horizontal (σθ) angles. The second part is the measurement of a test stand which contains four plates in white, light grey, dark grey and black colors, for the determination of a priori precisions of the range observations (σρ). The test stand measurement is performed in a recursive manner so that sensor-to-object distance, incidence angle and surface reflectivity are parameterized. The experiment was conducted with three TLSs, namely Faro Focus 3D X330, Riegl VZ400 and Z+F 5010x in the same location and atmospheric conditions. This procedure was followed by the computation of error ellipsoids of each point using the law of variance-covariance propagation. The direction and size of the error ellipsoids were computed by the principal components transformation. Validation of the proposed error model was performed in real world scenarios, which revealed feasibility of the model.