Nitric acid is used because all nitrate salts are soluble in water. If we use H2SO4 or HCl they will produce sulphate or chloride salts. Some metal sulphates and chlorides are not very soluble in water. 

It is reported fact that the  plant extracts are   reducing agents[ contain alkaloids, phenolic compounds, terpenoids)

When ever we start a reaction with any plant extract, we bring the solution  almost to neutral state so that thereafter, depending upon our research problem  we may adjust the pH of reaction  medium after adding our own chemicals. So we need an oxidizing agent. But the oxidiging agent should be such that  after making the plant extract neutral, no part of the oxidizing agent should be left in the reaction mixture lest it may react with the reaction medium and give unwanted peaks . HNO3, one of the strongest oxidizing agent is best suited in the sense that it  changes to the GASEOUS PRODUCT- NO2(g) WHICH LEAVES THE REACTION MEDIUM.

HCl  ,ITSELF, BEING A REDUCING AGENT  IS UNSUITABLE

H2SO4, IS HARDLY USED AS OXIDIZING AGENT.  MORE OVER,the presence of SO4^-2  may create problems by giving addition unwanted/ unexplained  mass peaks of its own or of its dissociation species . 

thanks for sharing....

Nitric acid is used because all nitrate salts are soluble in water. If we use H2SO4 or HCl they will produce sulphate or chloride salts. Some metal sulphates and chlorides are not very soluble in water. 

The triple acid digestion method - sample (1 g) will be  weighed into a micro-kjeldahl digestion flask to which  mixture of concentrated HNO3, H2SO4, and 60 % HClO4 (9:2:1 v/v) were added. The flask was put on a heating block and digested to a clear solution, it was cooled and the content was transferred into a  volumetric flask and made-up to the volume mark with distilled water (Sahrawat et al., 2002). triple acid digestion method is a best method for quantification.

Nitric acid is a strong mineral acid that produces soluble salts, useful for keeping the elements of interest in solution until they reach the plasma of the ICPMS or flame of the AAS. Nitric acid also an oxidising agent, additioanlly breaking down the organic components better than some other acids.

HCl is also effective (hence its presence as stomach acid for example), but for laboratory purposes it is less efficient than HNO3. In combination with HNO3 (as Aqua regia and similar mixtures) however it is extremely reactive and can dissolve some solid metals which neither acid can on their own.

H2SO4 is also added to HNO3 in some digestion protocols, but neither HCl or H2SO4 are as easliy purified as HNO3: the latter can be scrubbed of contaminating elements to concentrations of parts per billiion or less, meaning the analyses are much less prone to errors.

Here is the procedure I have used in the past:

Article A cost-effective acid digestion method using closed polyprop...

yoI can use nitric acid or Hcl or even mixed but not sulfaric acid. some acid solutions might damage the instrument tubes.

In digestion process youn can use nitric acid or perchloric acid because they are voletial acids prof Dr fathi

Nitric acid is a better option and more better when mixed with HCl in the ratio of 3:1 as aqua regia, this is because the products of this combination are nitrosyl chloride and chlorine which are strong oxidizing agents.

May i know what are the Interested elements(Metals) that you want to estimate?

In Graphite Furnace Atomic Absorption Spectrophotometry (GFAAS), Hydrochloric acid creates some problem in graphite tube. From my experience, I found that when I use HCl, the atomization/ vaporization of liq. sample did not function properly.The HCl destroy the graphite tube quickly. If atomization does not work properly, then it affect the final result. In this cause you find that, In USEPA method they recommended to use HNO3 in place of HCl.

Source: USEPA method

Very good explanations are given by all, thanks to all.

Obviously, HNO3 is a basic acid for digestion/dissolution of any biological material, but for several elements you need some HCl or HF to keep them in solution.