Who are writing the job description for senior management?

Usually it is the HR department in most small /SME / larger firms that performs the job analysis function and coordinates the writing of job descriptions, the entire process usually requires some input from other levels of the company hierarchy - Top management/ decision makers, Job analysts, Supervisors/Project managers, Outside consultants (specialists for JD preparation)

Human Resource department is responsible for that.

That's a good question. In MNCs, the job descrption is written by recruitment agencies, they are informed of the required specifications and qualifications the senior management candidate would need. Most of the time, the interview process is held by the recruitment agency, after you pass that, only then is your CV given to the organisation (MNC). For small businesses, it is written by the MD or one of the HR officials within the company, the interviews are held by them as well.